Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(296,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.296");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(104\) |
Relative dimension: | \(52\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 296.20 | ||
Character | \(\chi\) | \(=\) | 429.296 |
Dual form | 429.2.t.a.329.20 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.716153 | + | 0.413471i | −0.506397 | + | 0.292368i | −0.731351 | − | 0.682001i | \(-0.761110\pi\) |
0.224955 | + | 0.974369i | \(0.427777\pi\) | |||||||
\(3\) | 1.20308 | − | 1.24603i | 0.694599 | − | 0.719397i | ||||
\(4\) | −0.658083 | + | 1.13983i | −0.329042 | + | 0.569917i | ||||
\(5\) | 3.60945 | 1.61420 | 0.807099 | − | 0.590417i | \(-0.201037\pi\) | ||||
0.807099 | + | 0.590417i | \(0.201037\pi\) | |||||||
\(6\) | −0.346391 | + | 1.38979i | −0.141413 | + | 0.567379i | ||||
\(7\) | 1.45351 | − | 2.51755i | 0.549375 | − | 0.951545i | −0.448943 | − | 0.893561i | \(-0.648199\pi\) |
0.998317 | − | 0.0579844i | \(-0.0184674\pi\) | |||||||
\(8\) | − | 2.74228i | − | 0.969542i | ||||||
\(9\) | −0.105197 | − | 2.99816i | −0.0350655 | − | 0.999385i | ||||
\(10\) | −2.58492 | + | 1.49241i | −0.817424 | + | 0.471940i | ||||
\(11\) | −3.01848 | + | 1.37434i | −0.910105 | + | 0.414378i | ||||
\(12\) | 0.628544 | + | 2.19131i | 0.181445 | + | 0.632575i | ||||
\(13\) | 2.11573 | − | 2.91953i | 0.586799 | − | 0.809733i | ||||
\(14\) | 2.40394i | 0.642479i | ||||||||
\(15\) | 4.34246 | − | 4.49750i | 1.12122 | − | 1.16125i | ||||
\(16\) | −0.182314 | − | 0.315778i | −0.0455786 | − | 0.0789444i | ||||
\(17\) | −0.309839 | + | 0.536657i | −0.0751470 | + | 0.130158i | −0.901150 | − | 0.433507i | \(-0.857276\pi\) |
0.826003 | + | 0.563665i | \(0.190609\pi\) | |||||||
\(18\) | 1.31499 | + | 2.10364i | 0.309945 | + | 0.495833i | ||||
\(19\) | −1.18049 | + | 2.04467i | −0.270823 | + | 0.469079i | −0.969073 | − | 0.246775i | \(-0.920629\pi\) |
0.698250 | + | 0.715854i | \(0.253962\pi\) | |||||||
\(20\) | −2.37532 | + | 4.11418i | −0.531138 | + | 0.919958i | ||||
\(21\) | −1.38826 | − | 4.83994i | −0.302944 | − | 1.05616i | ||||
\(22\) | 1.59344 | − | 2.23229i | 0.339723 | − | 0.475925i | ||||
\(23\) | −5.10705 | + | 2.94856i | −1.06489 | + | 0.614817i | −0.926782 | − | 0.375600i | \(-0.877437\pi\) |
−0.138112 | + | 0.990417i | \(0.544103\pi\) | |||||||
\(24\) | −3.41697 | − | 3.29918i | −0.697486 | − | 0.673442i | ||||
\(25\) | 8.02816 | 1.60563 | ||||||||
\(26\) | −0.308046 | + | 2.96563i | −0.0604127 | + | 0.581607i | ||||
\(27\) | −3.86236 | − | 3.47594i | −0.743312 | − | 0.668945i | ||||
\(28\) | 1.91306 | + | 3.31352i | 0.361534 | + | 0.626196i | ||||
\(29\) | 3.36278 | + | 5.82450i | 0.624452 | + | 1.08158i | 0.988647 | + | 0.150259i | \(0.0480109\pi\) |
−0.364195 | + | 0.931323i | \(0.618656\pi\) | |||||||
\(30\) | −1.25028 | + | 5.01638i | −0.228269 | + | 0.915862i | ||||
\(31\) | − | 5.67006i | − | 1.01837i | −0.860656 | − | 0.509186i | \(-0.829946\pi\) | ||
0.860656 | − | 0.509186i | \(-0.170054\pi\) | |||||||
\(32\) | 5.01089 | + | 2.89304i | 0.885809 | + | 0.511422i | ||||
\(33\) | −1.91900 | + | 5.41456i | −0.334055 | + | 0.942554i | ||||
\(34\) | − | 0.512438i | − | 0.0878824i | ||||||
\(35\) | 5.24637 | − | 9.08699i | 0.886799 | − | 1.53598i | ||||
\(36\) | 3.48663 | + | 1.85313i | 0.581104 | + | 0.308855i | ||||
\(37\) | 0.225314 | − | 0.130085i | 0.0370414 | − | 0.0213859i | −0.481365 | − | 0.876520i | \(-0.659859\pi\) |
0.518406 | + | 0.855134i | \(0.326525\pi\) | |||||||
\(38\) | − | 1.95239i | − | 0.316720i | ||||||
\(39\) | −1.09244 | − | 6.14871i | −0.174930 | − | 0.984581i | ||||
\(40\) | − | 9.89813i | − | 1.56503i | ||||||
\(41\) | −2.92623 | + | 1.68946i | −0.457000 | + | 0.263849i | −0.710782 | − | 0.703412i | \(-0.751659\pi\) |
0.253782 | + | 0.967261i | \(0.418325\pi\) | |||||||
\(42\) | 2.99538 | + | 2.89213i | 0.462198 | + | 0.446265i | ||||
\(43\) | 8.07839 | + | 4.66406i | 1.23194 | + | 0.711263i | 0.967435 | − | 0.253121i | \(-0.0814570\pi\) |
0.264508 | + | 0.964383i | \(0.414790\pi\) | |||||||
\(44\) | 0.419892 | − | 4.34499i | 0.0633011 | − | 0.655032i | ||||
\(45\) | −0.379702 | − | 10.8217i | −0.0566027 | − | 1.61320i | ||||
\(46\) | 2.43829 | − | 4.22324i | 0.359506 | − | 0.622682i | ||||
\(47\) | 6.20944 | 0.905740 | 0.452870 | − | 0.891577i | \(-0.350400\pi\) | ||||
0.452870 | + | 0.891577i | \(0.350400\pi\) | |||||||
\(48\) | −0.612808 | − | 0.152736i | −0.0884512 | − | 0.0220456i | ||||
\(49\) | −0.725377 | − | 1.25639i | −0.103625 | − | 0.179484i | ||||
\(50\) | −5.74939 | + | 3.31941i | −0.813087 | + | 0.469436i | ||||
\(51\) | 0.295931 | + | 1.03171i | 0.0414387 | + | 0.144468i | ||||
\(52\) | 1.93545 | + | 4.33288i | 0.268399 | + | 0.600862i | ||||
\(53\) | 0.712815i | 0.0979126i | 0.998801 | + | 0.0489563i | \(0.0155895\pi\) | ||||
−0.998801 | + | 0.0489563i | \(0.984410\pi\) | |||||||
\(54\) | 4.20324 | + | 0.892332i | 0.571989 | + | 0.121431i | ||||
\(55\) | −10.8951 | + | 4.96061i | −1.46909 | + | 0.668889i | ||||
\(56\) | −6.90383 | − | 3.98593i | −0.922562 | − | 0.532642i | ||||
\(57\) | 1.12750 | + | 3.93083i | 0.149341 | + | 0.520651i | ||||
\(58\) | −4.81652 | − | 2.78082i | −0.632440 | − | 0.365140i | ||||
\(59\) | 0.121513 | − | 0.210467i | 0.0158196 | − | 0.0274004i | −0.858007 | − | 0.513638i | \(-0.828298\pi\) |
0.873827 | + | 0.486237i | \(0.161631\pi\) | |||||||
\(60\) | 2.26870 | + | 7.90942i | 0.292888 | + | 1.02110i | ||||
\(61\) | −8.04868 | − | 4.64691i | −1.03053 | − | 0.594975i | −0.113392 | − | 0.993550i | \(-0.536172\pi\) |
−0.917136 | + | 0.398575i | \(0.869505\pi\) | |||||||
\(62\) | 2.34440 | + | 4.06063i | 0.297740 | + | 0.515700i | ||||
\(63\) | −7.70091 | − | 4.09301i | −0.970224 | − | 0.515670i | ||||
\(64\) | −4.05550 | −0.506937 | ||||||||
\(65\) | 7.63664 | − | 10.5379i | 0.947209 | − | 1.30707i | ||||
\(66\) | −0.864468 | − | 4.67110i | −0.106409 | − | 0.574973i | ||||
\(67\) | −4.43422 | + | 2.56010i | −0.541726 | + | 0.312765i | −0.745778 | − | 0.666194i | \(-0.767922\pi\) |
0.204052 | + | 0.978960i | \(0.434589\pi\) | |||||||
\(68\) | −0.407800 | − | 0.706330i | −0.0494530 | − | 0.0856551i | ||||
\(69\) | −2.47019 | + | 9.91091i | −0.297376 | + | 1.19313i | ||||
\(70\) | 8.67690i | 1.03709i | ||||||||
\(71\) | −7.67720 | + | 13.2973i | −0.911116 | + | 1.57810i | −0.0986246 | + | 0.995125i | \(0.531444\pi\) |
−0.812491 | + | 0.582974i | \(0.801889\pi\) | |||||||
\(72\) | −8.22177 | + | 0.288478i | −0.968945 | + | 0.0339975i | ||||
\(73\) | 13.2442 | 1.55011 | 0.775057 | − | 0.631891i | \(-0.217721\pi\) | ||||
0.775057 | + | 0.631891i | \(0.217721\pi\) | |||||||
\(74\) | −0.107573 | + | 0.186322i | −0.0125051 | + | 0.0216595i | ||||
\(75\) | 9.65852 | − | 10.0034i | 1.11527 | − | 1.15509i | ||||
\(76\) | −1.55372 | − | 2.69112i | −0.178224 | − | 0.308693i | ||||
\(77\) | −0.927415 | + | 9.59678i | −0.105689 | + | 1.09365i | ||||
\(78\) | 3.32466 | + | 3.95172i | 0.376444 | + | 0.447444i | ||||
\(79\) | − | 0.316398i | − | 0.0355975i | −0.999842 | − | 0.0177988i | \(-0.994334\pi\) | ||
0.999842 | − | 0.0177988i | \(-0.00566582\pi\) | |||||||
\(80\) | −0.658055 | − | 1.13979i | −0.0735728 | − | 0.127432i | ||||
\(81\) | −8.97787 | + | 0.630791i | −0.997541 | + | 0.0700879i | ||||
\(82\) | 1.39709 | − | 2.41982i | 0.154282 | − | 0.267225i | ||||
\(83\) | 15.6297i | 1.71558i | 0.513997 | + | 0.857792i | \(0.328164\pi\) | ||||
−0.513997 | + | 0.857792i | \(0.671836\pi\) | |||||||
\(84\) | 6.43032 | + | 1.60269i | 0.701605 | + | 0.174868i | ||||
\(85\) | −1.11835 | + | 1.93704i | −0.121302 | + | 0.210101i | ||||
\(86\) | −7.71382 | −0.831802 | ||||||||
\(87\) | 11.3032 | + | 2.81721i | 1.21183 | + | 0.302036i | ||||
\(88\) | 3.76882 | + | 8.27750i | 0.401757 | + | 0.882384i | ||||
\(89\) | 5.29627 | + | 9.17341i | 0.561403 | + | 0.972379i | 0.997374 | + | 0.0724184i | \(0.0230717\pi\) |
−0.435971 | + | 0.899961i | \(0.643595\pi\) | |||||||
\(90\) | 4.74639 | + | 7.59300i | 0.500313 | + | 0.800372i | ||||
\(91\) | −4.27484 | − | 9.57003i | −0.448125 | − | 1.00321i | ||||
\(92\) | − | 7.76159i | − | 0.809202i | ||||||
\(93\) | −7.06508 | − | 6.82153i | −0.732614 | − | 0.707360i | ||||
\(94\) | −4.44691 | + | 2.56742i | −0.458664 | + | 0.264810i | ||||
\(95\) | −4.26092 | + | 7.38013i | −0.437161 | + | 0.757186i | ||||
\(96\) | 9.63333 | − | 2.76318i | 0.983198 | − | 0.282016i | ||||
\(97\) | 12.7818 | + | 7.37955i | 1.29779 | + | 0.749279i | 0.980022 | − | 0.198889i | \(-0.0637333\pi\) |
0.317768 | + | 0.948168i | \(0.397067\pi\) | |||||||
\(98\) | 1.03896 | + | 0.599844i | 0.104951 | + | 0.0605934i | ||||
\(99\) | 4.43801 | + | 8.90528i | 0.446037 | + | 0.895015i | ||||
\(100\) | −5.28320 | + | 9.15077i | −0.528320 | + | 0.915077i | ||||
\(101\) | −7.75309 | − | 13.4287i | −0.771461 | − | 1.33621i | −0.936762 | − | 0.349967i | \(-0.886193\pi\) |
0.165301 | − | 0.986243i | \(-0.447140\pi\) | |||||||
\(102\) | −0.638515 | − | 0.616504i | −0.0632224 | − | 0.0610430i | ||||
\(103\) | −18.8109 | −1.85349 | −0.926747 | − | 0.375686i | \(-0.877407\pi\) | ||||
−0.926747 | + | 0.375686i | \(0.877407\pi\) | |||||||
\(104\) | −8.00617 | − | 5.80193i | −0.785070 | − | 0.568926i | ||||
\(105\) | −5.01088 | − | 17.4695i | −0.489012 | − | 1.70485i | ||||
\(106\) | −0.294728 | − | 0.510484i | −0.0286265 | − | 0.0495826i | ||||
\(107\) | −4.77385 | − | 8.26856i | −0.461506 | − | 0.799352i | 0.537530 | − | 0.843244i | \(-0.319357\pi\) |
−0.999036 | + | 0.0438927i | \(0.986024\pi\) | |||||||
\(108\) | 6.50375 | − | 2.11499i | 0.625824 | − | 0.203515i | ||||
\(109\) | −6.66701 | −0.638584 | −0.319292 | − | 0.947656i | \(-0.603445\pi\) | ||||
−0.319292 | + | 0.947656i | \(0.603445\pi\) | |||||||
\(110\) | 5.75145 | − | 8.05734i | 0.548380 | − | 0.768238i | ||||
\(111\) | 0.108981 | − | 0.437252i | 0.0103440 | − | 0.0415021i | ||||
\(112\) | −1.05998 | −0.100159 | ||||||||
\(113\) | −8.81795 | − | 5.09105i | −0.829523 | − | 0.478926i | 0.0241661 | − | 0.999708i | \(-0.492307\pi\) |
−0.853689 | + | 0.520782i | \(0.825640\pi\) | |||||||
\(114\) | −2.43274 | − | 2.34888i | −0.227847 | − | 0.219993i | ||||
\(115\) | −18.4337 | + | 10.6427i | −1.71895 | + | 0.992436i | ||||
\(116\) | −8.85195 | −0.821883 | ||||||||
\(117\) | −8.97578 | − | 6.03617i | −0.829811 | − | 0.558044i | ||||
\(118\) | 0.200968i | 0.0185006i | ||||||||
\(119\) | 0.900708 | + | 1.56007i | 0.0825678 | + | 0.143012i | ||||
\(120\) | −12.3334 | − | 11.9082i | −1.12588 | − | 1.08707i | ||||
\(121\) | 7.22239 | − | 8.29681i | 0.656581 | − | 0.754256i | ||||
\(122\) | 7.68544 | 0.695807 | ||||||||
\(123\) | −1.41537 | + | 5.67873i | −0.127619 | + | 0.512034i | ||||
\(124\) | 6.46292 | + | 3.73137i | 0.580388 | + | 0.335087i | ||||
\(125\) | 10.9300 | 0.977611 | ||||||||
\(126\) | 7.20737 | − | 0.252886i | 0.642084 | − | 0.0225288i | ||||
\(127\) | −11.2624 | + | 6.50233i | −0.999373 | + | 0.576988i | −0.908063 | − | 0.418834i | \(-0.862439\pi\) |
−0.0913103 | + | 0.995822i | \(0.529106\pi\) | |||||||
\(128\) | −7.11743 | + | 4.10925i | −0.629098 | + | 0.363210i | ||||
\(129\) | 15.5305 | − | 4.45470i | 1.36739 | − | 0.392215i | ||||
\(130\) | −1.11188 | + | 10.7043i | −0.0975180 | + | 0.938829i | ||||
\(131\) | −1.19424 | −0.104341 | −0.0521706 | − | 0.998638i | \(-0.516614\pi\) | ||||
−0.0521706 | + | 0.998638i | \(0.516614\pi\) | |||||||
\(132\) | −4.90884 | − | 5.75057i | −0.427259 | − | 0.500523i | ||||
\(133\) | 3.43170 | + | 5.94388i | 0.297566 | + | 0.515400i | ||||
\(134\) | 2.11705 | − | 3.66684i | 0.182885 | − | 0.316767i | ||||
\(135\) | −13.9410 | − | 12.5463i | −1.19985 | − | 1.07981i | ||||
\(136\) | 1.47166 | + | 0.849665i | 0.126194 | + | 0.0728582i | ||||
\(137\) | −0.795650 | + | 1.37811i | −0.0679769 | + | 0.117740i | −0.898011 | − | 0.439974i | \(-0.854988\pi\) |
0.830034 | + | 0.557713i | \(0.188321\pi\) | |||||||
\(138\) | −2.32884 | − | 8.11908i | −0.198244 | − | 0.691142i | ||||
\(139\) | −6.24093 | − | 3.60320i | −0.529349 | − | 0.305620i | 0.211402 | − | 0.977399i | \(-0.432197\pi\) |
−0.740751 | + | 0.671779i | \(0.765530\pi\) | |||||||
\(140\) | 6.90510 | + | 11.9600i | 0.583588 | + | 1.01080i | ||||
\(141\) | 7.47045 | − | 7.73717i | 0.629126 | − | 0.651587i | ||||
\(142\) | − | 12.6972i | − | 1.06552i | ||||||
\(143\) | −2.37386 | + | 11.7203i | −0.198512 | + | 0.980098i | ||||
\(144\) | −0.927571 | + | 0.579825i | −0.0772976 | + | 0.0483188i | ||||
\(145\) | 12.1378 | + | 21.0233i | 1.00799 | + | 1.74589i | ||||
\(146\) | −9.48486 | + | 5.47609i | −0.784972 | + | 0.453204i | ||||
\(147\) | −2.43819 | − | 0.607694i | −0.201098 | − | 0.0501217i | ||||
\(148\) | 0.342428i | 0.0281474i | ||||||||
\(149\) | −0.645717 | − | 0.372805i | −0.0528992 | − | 0.0305414i | 0.473317 | − | 0.880892i | \(-0.343056\pi\) |
−0.526216 | + | 0.850351i | \(0.676390\pi\) | |||||||
\(150\) | −2.78088 | + | 11.1575i | −0.227058 | + | 0.911002i | ||||
\(151\) | 5.46182 | 0.444477 | 0.222238 | − | 0.974992i | \(-0.428664\pi\) | ||||
0.222238 | + | 0.974992i | \(0.428664\pi\) | |||||||
\(152\) | 5.60704 | + | 3.23723i | 0.454791 | + | 0.262574i | ||||
\(153\) | 1.64158 | + | 0.872491i | 0.132714 | + | 0.0705367i | ||||
\(154\) | −3.30382 | − | 7.25622i | −0.266229 | − | 0.584723i | ||||
\(155\) | − | 20.4658i | − | 1.64385i | ||||||
\(156\) | 7.72742 | + | 2.80116i | 0.618689 | + | 0.224272i | ||||
\(157\) | 8.52908 | 0.680695 | 0.340347 | − | 0.940300i | \(-0.389455\pi\) | ||||
0.340347 | + | 0.940300i | \(0.389455\pi\) | |||||||
\(158\) | 0.130821 | + | 0.226589i | 0.0104076 | + | 0.0180265i | ||||
\(159\) | 0.888191 | + | 0.857573i | 0.0704381 | + | 0.0680100i | ||||
\(160\) | 18.0866 | + | 10.4423i | 1.42987 | + | 0.825536i | ||||
\(161\) | 17.1430i | 1.35106i | ||||||||
\(162\) | 6.16871 | − | 4.16383i | 0.484660 | − | 0.327141i | ||||
\(163\) | −11.4306 | − | 6.59946i | −0.895314 | − | 0.516910i | −0.0196371 | − | 0.999807i | \(-0.506251\pi\) |
−0.875677 | + | 0.482897i | \(0.839584\pi\) | |||||||
\(164\) | − | 4.44722i | − | 0.347270i | ||||||
\(165\) | −6.92653 | + | 19.5436i | −0.539230 | + | 1.52147i | ||||
\(166\) | −6.46243 | − | 11.1933i | −0.501582 | − | 0.868766i | ||||
\(167\) | 18.4673 | − | 10.6621i | 1.42904 | − | 0.825057i | 0.431996 | − | 0.901876i | \(-0.357810\pi\) |
0.997045 | + | 0.0768186i | \(0.0244762\pi\) | |||||||
\(168\) | −13.2724 | + | 3.80701i | −1.02399 | + | 0.293717i | ||||
\(169\) | −4.04735 | − | 12.3539i | −0.311335 | − | 0.950300i | ||||
\(170\) | − | 1.84962i | − | 0.141860i | ||||||
\(171\) | 6.25441 | + | 3.32420i | 0.478287 | + | 0.254208i | ||||
\(172\) | −10.6325 | + | 6.13868i | −0.810721 | + | 0.468070i | ||||
\(173\) | 5.03566 | − | 8.72202i | 0.382854 | − | 0.663123i | −0.608615 | − | 0.793466i | \(-0.708275\pi\) |
0.991469 | + | 0.130343i | \(0.0416078\pi\) | |||||||
\(174\) | −9.25966 | + | 2.65600i | −0.701973 | + | 0.201351i | ||||
\(175\) | 11.6690 | − | 20.2113i | 0.882094 | − | 1.52783i | ||||
\(176\) | 0.984296 | + | 0.702606i | 0.0741941 | + | 0.0529609i | ||||
\(177\) | −0.116059 | − | 0.404618i | −0.00872350 | − | 0.0304129i | ||||
\(178\) | −7.58588 | − | 4.37971i | −0.568585 | − | 0.328273i | ||||
\(179\) | 9.04701 | − | 5.22330i | 0.676205 | − | 0.390407i | −0.122218 | − | 0.992503i | \(-0.539001\pi\) |
0.798424 | + | 0.602096i | \(0.205667\pi\) | |||||||
\(180\) | 12.5848 | + | 6.68879i | 0.938017 | + | 0.498553i | ||||
\(181\) | 17.7170 | 1.31690 | 0.658448 | − | 0.752626i | \(-0.271213\pi\) | ||||
0.658448 | + | 0.752626i | \(0.271213\pi\) | |||||||
\(182\) | 7.01837 | + | 5.08608i | 0.520236 | + | 0.377006i | ||||
\(183\) | −15.4734 | + | 4.43832i | −1.14383 | + | 0.328090i | ||||
\(184\) | 8.08577 | + | 14.0050i | 0.596091 | + | 1.03246i | ||||
\(185\) | 0.813261 | − | 0.469537i | 0.0597922 | − | 0.0345210i | ||||
\(186\) | 7.88018 | + | 1.96405i | 0.577803 | + | 0.144011i | ||||
\(187\) | 0.197694 | − | 2.04571i | 0.0144568 | − | 0.149597i | ||||
\(188\) | −4.08633 | + | 7.07773i | −0.298026 | + | 0.516197i | ||||
\(189\) | −14.3648 | + | 4.67138i | −1.04489 | + | 0.339793i | ||||
\(190\) | − | 7.04707i | − | 0.511248i | ||||||
\(191\) | −3.82809 | − | 2.21015i | −0.276991 | − | 0.159921i | 0.355070 | − | 0.934840i | \(-0.384457\pi\) |
−0.632060 | + | 0.774919i | \(0.717791\pi\) | |||||||
\(192\) | −4.87909 | + | 5.05328i | −0.352118 | + | 0.364689i | ||||
\(193\) | 0.123929 | + | 0.214651i | 0.00892061 | + | 0.0154509i | 0.870451 | − | 0.492255i | \(-0.163827\pi\) |
−0.861531 | + | 0.507706i | \(0.830494\pi\) | |||||||
\(194\) | −12.2049 | −0.876262 | ||||||||
\(195\) | −3.94311 | − | 22.1935i | −0.282372 | − | 1.58931i | ||||
\(196\) | 1.90943 | 0.136388 | ||||||||
\(197\) | −3.20326 | + | 1.84940i | −0.228223 | + | 0.131765i | −0.609752 | − | 0.792592i | \(-0.708731\pi\) |
0.381529 | + | 0.924357i | \(0.375398\pi\) | |||||||
\(198\) | −6.86037 | − | 4.54255i | −0.487545 | − | 0.322825i | ||||
\(199\) | 2.15254 | − | 3.72831i | 0.152590 | − | 0.264293i | −0.779589 | − | 0.626291i | \(-0.784572\pi\) |
0.932179 | + | 0.361998i | \(0.117905\pi\) | |||||||
\(200\) | − | 22.0155i | − | 1.55673i | ||||||
\(201\) | −2.14475 | + | 8.60518i | −0.151279 | + | 0.606963i | ||||
\(202\) | 11.1048 | + | 6.41136i | 0.781331 | + | 0.451101i | ||||
\(203\) | 19.5513 | 1.37223 | ||||||||
\(204\) | −1.37073 | − | 0.341640i | −0.0959701 | − | 0.0239196i | ||||
\(205\) | −10.5621 | + | 6.09803i | −0.737689 | + | 0.425905i | ||||
\(206\) | 13.4715 | − | 7.77777i | 0.938603 | − | 0.541903i | ||||
\(207\) | 9.37748 | + | 15.0016i | 0.651780 | + | 1.04268i | ||||
\(208\) | −1.30765 | − | 0.135828i | −0.0906693 | − | 0.00941800i | ||||
\(209\) | 0.753214 | − | 7.79417i | 0.0521009 | − | 0.539134i | ||||
\(210\) | 10.8117 | + | 10.4390i | 0.746078 | + | 0.720360i | ||||
\(211\) | −11.2825 | + | 6.51393i | −0.776716 | + | 0.448437i | −0.835265 | − | 0.549847i | \(-0.814686\pi\) |
0.0585490 | + | 0.998285i | \(0.481353\pi\) | |||||||
\(212\) | −0.812490 | − | 0.469092i | −0.0558021 | − | 0.0322173i | ||||
\(213\) | 7.33259 | + | 25.5638i | 0.502420 | + | 1.75160i | ||||
\(214\) | 6.83762 | + | 3.94770i | 0.467410 | + | 0.269859i | ||||
\(215\) | 29.1586 | + | 16.8347i | 1.98860 | + | 1.14812i | ||||
\(216\) | −9.53200 | + | 10.5917i | −0.648570 | + | 0.720671i | ||||
\(217\) | −14.2747 | − | 8.24148i | −0.969027 | − | 0.559468i | ||||
\(218\) | 4.77460 | − | 2.75662i | 0.323377 | − | 0.186702i | ||||
\(219\) | 15.9338 | − | 16.5027i | 1.07671 | − | 1.11515i | ||||
\(220\) | 1.51558 | − | 15.6830i | 0.102180 | − | 1.05735i | ||||
\(221\) | 0.911252 | + | 2.04001i | 0.0612974 | + | 0.137226i | ||||
\(222\) | 0.102744 | + | 0.358199i | 0.00689574 | + | 0.0240408i | ||||
\(223\) | −3.59489 | + | 2.07551i | −0.240732 | + | 0.138987i | −0.615513 | − | 0.788127i | \(-0.711051\pi\) |
0.374781 | + | 0.927113i | \(0.377718\pi\) | |||||||
\(224\) | 14.5668 | − | 8.41012i | 0.973283 | − | 0.561925i | ||||
\(225\) | −0.844535 | − | 24.0697i | −0.0563023 | − | 1.60465i | ||||
\(226\) | 8.42000 | 0.560090 | ||||||||
\(227\) | −7.31729 | − | 4.22464i | −0.485665 | − | 0.280399i | 0.237109 | − | 0.971483i | \(-0.423800\pi\) |
−0.722774 | + | 0.691084i | \(0.757133\pi\) | |||||||
\(228\) | −5.22248 | − | 1.30165i | −0.345867 | − | 0.0862038i | ||||
\(229\) | − | 15.9604i | − | 1.05469i | −0.849650 | − | 0.527346i | \(-0.823187\pi\) | ||
0.849650 | − | 0.527346i | \(-0.176813\pi\) | |||||||
\(230\) | 8.80089 | − | 15.2436i | 0.580313 | − | 1.00513i | ||||
\(231\) | 10.8422 | + | 12.7013i | 0.713361 | + | 0.835683i | ||||
\(232\) | 15.9724 | − | 9.22167i | 1.04864 | − | 0.605432i | ||||
\(233\) | −14.4909 | −0.949331 | −0.474666 | − | 0.880166i | \(-0.657431\pi\) | ||||
−0.474666 | + | 0.880166i | \(0.657431\pi\) | |||||||
\(234\) | 8.92381 | + | 0.611595i | 0.583368 | + | 0.0399812i | ||||
\(235\) | 22.4127 | 1.46204 | ||||||||
\(236\) | 0.159931 | + | 0.277009i | 0.0104106 | + | 0.0180318i | ||||
\(237\) | −0.394242 | − | 0.380652i | −0.0256088 | − | 0.0247260i | ||||
\(238\) | −1.29009 | − | 0.744833i | −0.0836241 | − | 0.0482804i | ||||
\(239\) | 0.504548i | 0.0326365i | 0.999867 | + | 0.0163182i | \(0.00519449\pi\) | ||||
−0.999867 | + | 0.0163182i | \(0.994806\pi\) | |||||||
\(240\) | −2.21190 | − | 0.551294i | −0.142778 | − | 0.0355859i | ||||
\(241\) | −9.18385 | + | 15.9069i | −0.591584 | + | 1.02465i | 0.402435 | + | 0.915448i | \(0.368164\pi\) |
−0.994019 | + | 0.109205i | \(0.965169\pi\) | |||||||
\(242\) | −1.74184 | + | 8.92803i | −0.111970 | + | 0.573916i | ||||
\(243\) | −10.0151 | + | 11.9456i | −0.642469 | + | 0.766311i | ||||
\(244\) | 10.5934 | − | 6.11610i | 0.678173 | − | 0.391543i | ||||
\(245\) | −2.61821 | − | 4.53488i | −0.167272 | − | 0.289723i | ||||
\(246\) | −1.33437 | − | 4.65205i | −0.0850765 | − | 0.296604i | ||||
\(247\) | 3.47187 | + | 7.77244i | 0.220910 | + | 0.494549i | ||||
\(248\) | −15.5489 | −0.987354 | ||||||||
\(249\) | 19.4751 | + | 18.8038i | 1.23419 | + | 1.19164i | ||||
\(250\) | −7.82756 | + | 4.51925i | −0.495059 | + | 0.285822i | ||||
\(251\) | 10.8243 | + | 6.24940i | 0.683222 | + | 0.394459i | 0.801068 | − | 0.598573i | \(-0.204265\pi\) |
−0.117846 | + | 0.993032i | \(0.537599\pi\) | |||||||
\(252\) | 9.73319 | − | 6.08422i | 0.613133 | − | 0.383270i | ||||
\(253\) | 11.3632 | − | 15.9190i | 0.714398 | − | 1.00082i | ||||
\(254\) | 5.37705 | − | 9.31332i | 0.337386 | − | 0.584370i | ||||
\(255\) | 1.06815 | + | 3.72392i | 0.0668902 | + | 0.233201i | ||||
\(256\) | 7.45361 | − | 12.9100i | 0.465851 | − | 0.806877i | ||||
\(257\) | 8.57172 | − | 4.94889i | 0.534689 | − | 0.308703i | −0.208235 | − | 0.978079i | \(-0.566772\pi\) |
0.742924 | + | 0.669376i | \(0.233438\pi\) | |||||||
\(258\) | −9.28034 | + | 9.61167i | −0.577769 | + | 0.598396i | ||||
\(259\) | − | 0.756320i | − | 0.0469954i | ||||||
\(260\) | 6.98594 | + | 15.6393i | 0.433249 | + | 0.969910i | ||||
\(261\) | 17.1090 | − | 10.6948i | 1.05902 | − | 0.661994i | ||||
\(262\) | 0.855258 | − | 0.493783i | 0.0528380 | − | 0.0305060i | ||||
\(263\) | −5.57568 | − | 9.65736i | −0.343811 | − | 0.595498i | 0.641326 | − | 0.767269i | \(-0.278385\pi\) |
−0.985137 | + | 0.171770i | \(0.945051\pi\) | |||||||
\(264\) | 14.8482 | + | 5.26242i | 0.913845 | + | 0.323880i | ||||
\(265\) | 2.57287i | 0.158050i | ||||||||
\(266\) | −4.91525 | − | 2.83782i | −0.301373 | − | 0.173998i | ||||
\(267\) | 17.8022 | + | 4.43702i | 1.08948 | + | 0.271541i | ||||
\(268\) | − | 6.73903i | − | 0.411652i | ||||||
\(269\) | −0.197250 | − | 0.113882i | −0.0120266 | − | 0.00694353i | 0.493975 | − | 0.869476i | \(-0.335544\pi\) |
−0.506001 | + | 0.862533i | \(0.668877\pi\) | |||||||
\(270\) | 15.1714 | + | 3.22083i | 0.923303 | + | 0.196014i | ||||
\(271\) | −2.56137 | − | 4.43643i | −0.155592 | − | 0.269494i | 0.777682 | − | 0.628658i | \(-0.216395\pi\) |
−0.933275 | + | 0.359164i | \(0.883062\pi\) | |||||||
\(272\) | 0.225952 | 0.0137004 | ||||||||
\(273\) | −17.0676 | − | 6.18693i | −1.03298 | − | 0.374450i | ||||
\(274\) | − | 1.31591i | − | 0.0794972i | ||||||
\(275\) | −24.2328 | + | 11.0334i | −1.46129 | + | 0.665340i | ||||
\(276\) | −9.67120 | − | 9.33781i | −0.582138 | − | 0.562070i | ||||
\(277\) | 0.815907 | + | 0.471064i | 0.0490231 | + | 0.0283035i | 0.524311 | − | 0.851527i | \(-0.324323\pi\) |
−0.475288 | + | 0.879830i | \(0.657656\pi\) | |||||||
\(278\) | 5.95928 | 0.357414 | ||||||||
\(279\) | −16.9997 | + | 0.596470i | −1.01775 | + | 0.0357097i | ||||
\(280\) | −24.9190 | − | 14.3870i | −1.48920 | − | 0.859789i | ||||
\(281\) | 17.7047i | 1.05618i | 0.849190 | + | 0.528088i | \(0.177091\pi\) | ||||
−0.849190 | + | 0.528088i | \(0.822909\pi\) | |||||||
\(282\) | −2.15089 | + | 8.62981i | −0.128084 | + | 0.513898i | ||||
\(283\) | −4.13971 | + | 2.39006i | −0.246080 | + | 0.142075i | −0.617968 | − | 0.786203i | \(-0.712044\pi\) |
0.371888 | + | 0.928278i | \(0.378711\pi\) | |||||||
\(284\) | −10.1045 | − | 17.5015i | −0.599590 | − | 1.03852i | ||||
\(285\) | 4.06966 | + | 14.1881i | 0.241066 | + | 0.840433i | ||||
\(286\) | −3.14594 | − | 9.37503i | −0.186024 | − | 0.554357i | ||||
\(287\) | 9.82258i | 0.579808i | ||||||||
\(288\) | 8.14666 | − | 15.3278i | 0.480046 | − | 0.903198i | ||||
\(289\) | 8.30800 | + | 14.3899i | 0.488706 | + | 0.846463i | ||||
\(290\) | −17.3850 | − | 10.0372i | −1.02088 | − | 0.589407i | ||||
\(291\) | 24.5726 | − | 7.04830i | 1.44047 | − | 0.413178i | ||||
\(292\) | −8.71578 | + | 15.0962i | −0.510052 | + | 0.883436i | ||||
\(293\) | −14.7021 | − | 8.48825i | −0.858905 | − | 0.495889i | 0.00474047 | − | 0.999989i | \(-0.498491\pi\) |
−0.863645 | + | 0.504100i | \(0.831824\pi\) | |||||||
\(294\) | 1.99738 | − | 0.572919i | 0.116490 | − | 0.0334133i | ||||
\(295\) | 0.438596 | − | 0.759670i | 0.0255360 | − | 0.0442297i | ||||
\(296\) | −0.356730 | − | 0.617874i | −0.0207345 | − | 0.0359132i | ||||
\(297\) | 16.4356 | + | 5.18386i | 0.953688 | + | 0.300798i | ||||
\(298\) | 0.616576 | 0.0357173 | ||||||||
\(299\) | −2.19674 | + | 21.1486i | −0.127041 | + | 1.22305i | ||||
\(300\) | 5.04605 | + | 17.5922i | 0.291334 | + | 1.01568i | ||||
\(301\) | 23.4840 | − | 13.5585i | 1.35360 | − | 0.781499i | ||||
\(302\) | −3.91150 | + | 2.25831i | −0.225082 | + | 0.129951i | ||||
\(303\) | −26.0602 | − | 6.49525i | −1.49712 | − | 0.373142i | ||||
\(304\) | 0.860880 | 0.0493749 | ||||||||
\(305\) | −29.0513 | − | 16.7728i | −1.66347 | − | 0.960408i | ||||
\(306\) | −1.53637 | + | 0.0539067i | −0.0878284 | + | 0.00308164i | ||||
\(307\) | 26.7631 | 1.52745 | 0.763725 | − | 0.645542i | \(-0.223368\pi\) | ||||
0.763725 | + | 0.645542i | \(0.223368\pi\) | |||||||
\(308\) | −10.3284 | − | 7.37258i | −0.588516 | − | 0.420092i | ||||
\(309\) | −22.6310 | + | 23.4390i | −1.28743 | + | 1.33340i | ||||
\(310\) | 8.46202 | + | 14.6566i | 0.480610 | + | 0.832442i | ||||
\(311\) | 0.437159i | 0.0247890i | 0.999923 | + | 0.0123945i | \(0.00394539\pi\) | ||||
−0.999923 | + | 0.0123945i | \(0.996055\pi\) | |||||||
\(312\) | −16.8615 | + | 2.99577i | −0.954592 | + | 0.169602i | ||||
\(313\) | −14.0254 | −0.792764 | −0.396382 | − | 0.918086i | \(-0.629734\pi\) | ||||
−0.396382 | + | 0.918086i | \(0.629734\pi\) | |||||||
\(314\) | −6.10813 | + | 3.52653i | −0.344701 | + | 0.199014i | ||||
\(315\) | −27.7961 | − | 14.7735i | −1.56613 | − | 0.832394i | ||||
\(316\) | 0.360641 | + | 0.208216i | 0.0202876 | + | 0.0117131i | ||||
\(317\) | −1.32272 | −0.0742914 | −0.0371457 | − | 0.999310i | \(-0.511827\pi\) | ||||
−0.0371457 | + | 0.999310i | \(0.511827\pi\) | |||||||
\(318\) | −0.990662 | − | 0.246912i | −0.0555536 | − | 0.0138462i | ||||
\(319\) | −18.1553 | − | 12.9595i | −1.01650 | − | 0.725594i | ||||
\(320\) | −14.6381 | −0.818297 | ||||||||
\(321\) | −16.0462 | − | 3.99936i | −0.895613 | − | 0.223222i | ||||
\(322\) | −7.08814 | − | 12.2770i | −0.395007 | − | 0.684172i | ||||
\(323\) | −0.731523 | − | 1.26704i | −0.0407030 | − | 0.0704997i | ||||
\(324\) | 5.18919 | − | 10.6484i | 0.288288 | − | 0.591577i | ||||
\(325\) | 16.9854 | − | 23.4385i | 0.942183 | − | 1.30013i | ||||
\(326\) | 10.9147 | 0.604512 | ||||||||
\(327\) | −8.02095 | + | 8.30731i | −0.443559 | + | 0.459396i | ||||
\(328\) | 4.63297 | + | 8.02453i | 0.255813 | + | 0.443081i | ||||
\(329\) | 9.02548 | − | 15.6326i | 0.497591 | − | 0.861852i | ||||
\(330\) | −3.12026 | − | 16.8601i | −0.171765 | − | 0.928120i | ||||
\(331\) | −19.4419 | − | 11.2248i | −1.06862 | − | 0.616971i | −0.140819 | − | 0.990035i | \(-0.544974\pi\) |
−0.927805 | + | 0.373064i | \(0.878307\pi\) | |||||||
\(332\) | −17.8153 | − | 10.2857i | −0.977740 | − | 0.564498i | ||||
\(333\) | −0.413718 | − | 0.661842i | −0.0226716 | − | 0.0362687i | ||||
\(334\) | −8.81693 | + | 15.2714i | −0.482441 | + | 0.835612i | ||||
\(335\) | −16.0051 | + | 9.24055i | −0.874452 | + | 0.504865i | ||||
\(336\) | −1.27524 | + | 1.32077i | −0.0695702 | + | 0.0720540i | ||||
\(337\) | − | 14.1245i | − | 0.769412i | −0.923039 | − | 0.384706i | \(-0.874303\pi\) | ||
0.923039 | − | 0.384706i | \(-0.125697\pi\) | |||||||
\(338\) | 8.00650 | + | 7.17382i | 0.435496 | + | 0.390204i | ||||
\(339\) | −16.9523 | + | 4.86252i | −0.920724 | + | 0.264096i | ||||
\(340\) | −1.47194 | − | 2.54947i | −0.0798269 | − | 0.138264i | ||||
\(341\) | 7.79257 | + | 17.1149i | 0.421992 | + | 0.926825i | ||||
\(342\) | −5.85357 | + | 0.205385i | −0.316525 | + | 0.0111059i | ||||
\(343\) | 16.1318 | 0.871033 | ||||||||
\(344\) | 12.7902 | − | 22.1532i | 0.689599 | − | 1.19442i | ||||
\(345\) | −8.91605 | + | 35.7730i | −0.480024 | + | 1.92595i | ||||
\(346\) | 8.32840i | 0.447737i | ||||||||
\(347\) | 11.7907 | − | 20.4220i | 0.632955 | − | 1.09631i | −0.353989 | − | 0.935250i | \(-0.615175\pi\) |
0.986944 | − | 0.161061i | \(-0.0514917\pi\) | |||||||
\(348\) | −10.6496 | + | 11.0298i | −0.570879 | + | 0.591260i | ||||
\(349\) | 12.2094 | + | 21.1474i | 0.653556 | + | 1.13199i | 0.982254 | + | 0.187557i | \(0.0600571\pi\) |
−0.328697 | + | 0.944435i | \(0.606610\pi\) | |||||||
\(350\) | 19.2992i | 1.03158i | ||||||||
\(351\) | −18.3199 | + | 3.92212i | −0.977841 | + | 0.209347i | ||||
\(352\) | −19.1013 | − | 1.84591i | −1.01810 | − | 0.0983874i | ||||
\(353\) | −4.65200 | − | 8.05750i | −0.247601 | − | 0.428857i | 0.715259 | − | 0.698860i | \(-0.246309\pi\) |
−0.962860 | + | 0.270002i | \(0.912976\pi\) | |||||||
\(354\) | 0.250413 | + | 0.241781i | 0.0133093 | + | 0.0128505i | ||||
\(355\) | −27.7105 | + | 47.9960i | −1.47072 | + | 2.54736i | ||||
\(356\) | −13.9415 | −0.738900 | ||||||||
\(357\) | 3.02753 | + | 0.754580i | 0.160234 | + | 0.0399366i | ||||
\(358\) | −4.31936 | + | 7.48136i | −0.228285 | + | 0.395402i | ||||
\(359\) | − | 5.02549i | − | 0.265235i | −0.991167 | − | 0.132618i | \(-0.957662\pi\) | ||
0.991167 | − | 0.132618i | \(-0.0423382\pi\) | |||||||
\(360\) | −29.6761 | + | 1.04125i | −1.56407 | + | 0.0548786i | ||||
\(361\) | 6.71289 | + | 11.6271i | 0.353310 | + | 0.611951i | ||||
\(362\) | −12.6881 | + | 7.32548i | −0.666872 | + | 0.385019i | ||||
\(363\) | −1.64899 | − | 18.9811i | −0.0865494 | − | 0.996248i | ||||
\(364\) | 13.7214 | + | 1.42527i | 0.719199 | + | 0.0747047i | ||||
\(365\) | 47.8043 | 2.50219 | ||||||||
\(366\) | 9.24621 | − | 9.57632i | 0.483307 | − | 0.500562i | ||||
\(367\) | −10.9474 | − | 18.9615i | −0.571451 | − | 0.989782i | −0.996417 | − | 0.0845732i | \(-0.973047\pi\) |
0.424966 | − | 0.905209i | \(-0.360286\pi\) | |||||||
\(368\) | 1.86218 | + | 1.07513i | 0.0970727 | + | 0.0560450i | ||||
\(369\) | 5.37309 | + | 8.59556i | 0.279712 | + | 0.447467i | ||||
\(370\) | −0.388280 | + | 0.672520i | −0.0201857 | + | 0.0349627i | ||||
\(371\) | 1.79455 | + | 1.03608i | 0.0931683 | + | 0.0537907i | ||||
\(372\) | 12.4248 | − | 3.56388i | 0.644197 | − | 0.184778i | ||||
\(373\) | −17.6888 | − | 10.2126i | −0.915890 | − | 0.528789i | −0.0335684 | − | 0.999436i | \(-0.510687\pi\) |
−0.882322 | + | 0.470647i | \(0.844021\pi\) | |||||||
\(374\) | 0.704263 | + | 1.54678i | 0.0364166 | + | 0.0799822i | ||||
\(375\) | 13.1497 | − | 13.6192i | 0.679047 | − | 0.703291i | ||||
\(376\) | − | 17.0280i | − | 0.878153i | ||||||
\(377\) | 24.1196 | + | 2.50535i | 1.24222 | + | 0.129032i | ||||
\(378\) | 8.35594 | − | 9.28486i | 0.429783 | − | 0.477562i | ||||
\(379\) | −2.07421 | + | 1.19754i | −0.106545 | + | 0.0615137i | −0.552326 | − | 0.833629i | \(-0.686259\pi\) |
0.445781 | + | 0.895142i | \(0.352926\pi\) | |||||||
\(380\) | −5.60808 | − | 9.71348i | −0.287689 | − | 0.498291i | ||||
\(381\) | −5.44741 | + | 21.8561i | −0.279079 | + | 1.11972i | ||||
\(382\) | 3.65533 | 0.187023 | ||||||||
\(383\) | 4.75807 | − | 8.24123i | 0.243126 | − | 0.421107i | −0.718477 | − | 0.695551i | \(-0.755160\pi\) |
0.961603 | + | 0.274444i | \(0.0884937\pi\) | |||||||
\(384\) | −3.44258 | + | 13.8123i | −0.175678 | + | 0.704857i | ||||
\(385\) | −3.34746 | + | 34.6391i | −0.170602 | + | 1.76537i | ||||
\(386\) | −0.177504 | − | 0.102482i | −0.00903473 | − | 0.00521620i | ||||
\(387\) | 13.1338 | − | 24.7109i | 0.667626 | − | 1.25613i | ||||
\(388\) | −16.8229 | + | 9.71271i | −0.854054 | + | 0.493088i | ||||
\(389\) | 10.2200i | 0.518174i | 0.965854 | + | 0.259087i | \(0.0834216\pi\) | ||||
−0.965854 | + | 0.259087i | \(0.916578\pi\) | |||||||
\(390\) | 12.0002 | + | 14.2636i | 0.607655 | + | 0.722263i | ||||
\(391\) | − | 3.65432i | − | 0.184807i | ||||||
\(392\) | −3.44537 | + | 1.98918i | −0.174017 | + | 0.100469i | ||||
\(393\) | −1.43677 | + | 1.48806i | −0.0724752 | + | 0.0750628i | ||||
\(394\) | 1.52935 | − | 2.64891i | 0.0770476 | − | 0.133450i | ||||
\(395\) | − | 1.14202i | − | 0.0574614i | ||||||
\(396\) | −13.0711 | − | 0.801823i | −0.656849 | − | 0.0402931i | ||||
\(397\) | 25.4773 | + | 14.7093i | 1.27867 | + | 0.738239i | 0.976603 | − | 0.215049i | \(-0.0689912\pi\) |
0.302063 | + | 0.953288i | \(0.402325\pi\) | |||||||
\(398\) | 3.56005i | 0.178449i | ||||||||
\(399\) | 11.5349 | + | 2.87495i | 0.577467 | + | 0.143928i | ||||
\(400\) | −1.46365 | − | 2.53511i | −0.0731824 | − | 0.126756i | ||||
\(401\) | −9.74398 | − | 16.8771i | −0.486591 | − | 0.842801i | 0.513290 | − | 0.858215i | \(-0.328427\pi\) |
−0.999881 | + | 0.0154145i | \(0.995093\pi\) | |||||||
\(402\) | −2.02202 | − | 7.04942i | −0.100849 | − | 0.351593i | ||||
\(403\) | −16.5539 | − | 11.9963i | −0.824609 | − | 0.597579i | ||||
\(404\) | 20.4087 | 1.01537 | ||||||||
\(405\) | −32.4052 | + | 2.27681i | −1.61023 | + | 0.113136i | ||||
\(406\) | −14.0017 | + | 8.08390i | −0.694894 | + | 0.401197i | ||||
\(407\) | −0.501324 | + | 0.702317i | −0.0248497 | + | 0.0348126i | ||||
\(408\) | 2.82924 | − | 0.811526i | 0.140068 | − | 0.0401765i | ||||
\(409\) | 13.6097 | − | 23.5727i | 0.672956 | − | 1.16559i | −0.304105 | − | 0.952638i | \(-0.598357\pi\) |
0.977062 | − | 0.212956i | \(-0.0683092\pi\) | |||||||
\(410\) | 5.04272 | − | 8.73424i | 0.249042 | − | 0.431353i | ||||
\(411\) | 0.759935 | + | 2.64938i | 0.0374848 | + | 0.130684i | ||||
\(412\) | 12.3791 | − | 21.4413i | 0.609877 | − | 1.05634i | ||||
\(413\) | −0.353240 | − | 0.611830i | −0.0173818 | − | 0.0301062i | ||||
\(414\) | −12.9184 | − | 6.86609i | −0.634906 | − | 0.337450i | ||||
\(415\) | 56.4147i | 2.76929i | ||||||||
\(416\) | 19.0480 | − | 8.50857i | 0.933907 | − | 0.417167i | ||||
\(417\) | −11.9981 | + | 3.44147i | −0.587547 | + | 0.168529i | ||||
\(418\) | 2.68325 | + | 5.89325i | 0.131242 | + | 0.288248i | ||||
\(419\) | 19.6051 | − | 11.3190i | 0.957771 | − | 0.552969i | 0.0622847 | − | 0.998058i | \(-0.480161\pi\) |
0.895486 | + | 0.445089i | \(0.146828\pi\) | |||||||
\(420\) | 23.2099 | + | 5.78484i | 1.13253 | + | 0.282271i | ||||
\(421\) | 16.3608i | 0.797379i | 0.917086 | + | 0.398689i | \(0.130535\pi\) | ||||
−0.917086 | + | 0.398689i | \(0.869465\pi\) | |||||||
\(422\) | 5.38664 | − | 9.32994i | 0.262218 | − | 0.454174i | ||||
\(423\) | −0.653212 | − | 18.6169i | −0.0317602 | − | 0.905183i | ||||
\(424\) | 1.95474 | 0.0949304 | ||||||||
\(425\) | −2.48744 | + | 4.30837i | −0.120659 | + | 0.208987i | ||||
\(426\) | −15.8211 | − | 15.2757i | −0.766536 | − | 0.740112i | ||||
\(427\) | −23.3977 | + | 13.5086i | −1.13229 | + | 0.653729i | ||||
\(428\) | 12.5664 | 0.607419 | ||||||||
\(429\) | 11.7479 | + | 17.0583i | 0.567194 | + | 0.823584i | ||||
\(430\) | −27.8427 | −1.34269 | ||||||||
\(431\) | −2.91467 | + | 1.68278i | −0.140395 | + | 0.0810568i | −0.568552 | − | 0.822647i | \(-0.692496\pi\) |
0.428157 | + | 0.903704i | \(0.359163\pi\) | |||||||
\(432\) | −0.393461 | + | 1.85336i | −0.0189304 | + | 0.0891699i | ||||
\(433\) | −17.9077 | + | 31.0170i | −0.860587 | + | 1.49058i | 0.0107758 | + | 0.999942i | \(0.496570\pi\) |
−0.871363 | + | 0.490639i | \(0.836763\pi\) | |||||||
\(434\) | 13.6304 | 0.654283 | ||||||||
\(435\) | 40.7984 | + | 10.1686i | 1.95613 | + | 0.487546i | ||||
\(436\) | 4.38745 | − | 7.59928i | 0.210121 | − | 0.363940i | ||||
\(437\) | − | 13.9230i | − | 0.666026i | ||||||
\(438\) | −4.58766 | + | 18.4066i | −0.219207 | + | 0.879502i | ||||
\(439\) | 27.7633 | − | 16.0291i | 1.32507 | − | 0.765029i | 0.340537 | − | 0.940231i | \(-0.389391\pi\) |
0.984532 | + | 0.175202i | \(0.0560580\pi\) | |||||||
\(440\) | 13.6034 | + | 29.8773i | 0.648515 | + | 1.42434i | ||||
\(441\) | −3.69054 | + | 2.30696i | −0.175740 | + | 0.109855i | ||||
\(442\) | −1.49608 | − | 1.08418i | −0.0711613 | − | 0.0515693i | ||||
\(443\) | − | 16.7830i | − | 0.797385i | −0.917085 | − | 0.398693i | \(-0.869464\pi\) | ||
0.917085 | − | 0.398693i | \(-0.130536\pi\) | |||||||
\(444\) | 0.426676 | + | 0.411968i | 0.0202492 | + | 0.0195511i | ||||
\(445\) | 19.1166 | + | 33.1110i | 0.906216 | + | 1.56961i | ||||
\(446\) | 1.71633 | − | 2.97277i | 0.0812705 | − | 0.140765i | ||||
\(447\) | −1.24138 | + | 0.356070i | −0.0587151 | + | 0.0168416i | ||||
\(448\) | −5.89470 | + | 10.2099i | −0.278499 | + | 0.482374i | ||||
\(449\) | −2.77452 | + | 4.80562i | −0.130938 | + | 0.226791i | −0.924038 | − | 0.382300i | \(-0.875132\pi\) |
0.793101 | + | 0.609091i | \(0.208466\pi\) | |||||||
\(450\) | 10.5569 | + | 16.8884i | 0.497659 | + | 0.796126i | ||||
\(451\) | 6.51086 | − | 9.12122i | 0.306585 | − | 0.429501i | ||||
\(452\) | 11.6059 | − | 6.70067i | 0.545896 | − | 0.315173i | ||||
\(453\) | 6.57101 | − | 6.80561i | 0.308733 | − | 0.319756i | ||||
\(454\) | 6.98706 | 0.327919 | ||||||||
\(455\) | −15.4298 | − | 34.5426i | −0.723362 | − | 1.61938i | ||||
\(456\) | 10.7794 | − | 3.09192i | 0.504792 | − | 0.144792i | ||||
\(457\) | 9.72010 | + | 16.8357i | 0.454687 | + | 0.787541i | 0.998670 | − | 0.0515551i | \(-0.0164178\pi\) |
−0.543983 | + | 0.839096i | \(0.683084\pi\) | |||||||
\(458\) | 6.59916 | + | 11.4301i | 0.308359 | + | 0.534093i | ||||
\(459\) | 3.06210 | − | 0.995780i | 0.142927 | − | 0.0464790i | ||||
\(460\) | − | 28.0151i | − | 1.30621i | ||||||
\(461\) | −3.66287 | − | 2.11476i | −0.170597 | − | 0.0984940i | 0.412270 | − | 0.911061i | \(-0.364736\pi\) |
−0.582867 | + | 0.812567i | \(0.698069\pi\) | |||||||
\(462\) | −13.0163 | − | 4.61315i | −0.605571 | − | 0.214623i | ||||
\(463\) | − | 1.28884i | − | 0.0598974i | −0.999551 | − | 0.0299487i | \(-0.990466\pi\) | ||
0.999551 | − | 0.0299487i | \(-0.00953439\pi\) | |||||||
\(464\) | 1.22616 | − | 2.12378i | 0.0569232 | − | 0.0985939i | ||||
\(465\) | −25.5011 | − | 24.6220i | −1.18258 | − | 1.14182i | ||||
\(466\) | 10.3777 | − | 5.99157i | 0.480738 | − | 0.277554i | ||||
\(467\) | 7.43668i | 0.344128i | 0.985086 | + | 0.172064i | \(0.0550437\pi\) | ||||
−0.985086 | + | 0.172064i | \(0.944956\pi\) | |||||||
\(468\) | 12.7870 | − | 6.25860i | 0.591081 | − | 0.289304i | ||||
\(469\) | 14.8845i | 0.687302i | ||||||||
\(470\) | −16.0509 | + | 9.26700i | −0.740374 | + | 0.427455i | ||||
\(471\) | 10.2612 | − | 10.6275i | 0.472810 | − | 0.489690i | ||||
\(472\) | −0.577158 | − | 0.333222i | −0.0265659 | − | 0.0153378i | ||||
\(473\) | −30.7944 | − | 2.97592i | −1.41593 | − | 0.136833i | ||||
\(474\) | 0.439726 | + | 0.109597i | 0.0201973 | + | 0.00503397i | ||||
\(475\) | −9.47716 | + | 16.4149i | −0.434842 | + | 0.753168i | ||||
\(476\) | −2.37096 | −0.108673 | ||||||||
\(477\) | 2.13713 | − | 0.0749856i | 0.0978524 | − | 0.00343336i | ||||
\(478\) | −0.208616 | − | 0.361333i | −0.00954186 | − | 0.0165270i | ||||
\(479\) | −7.29276 | + | 4.21048i | −0.333215 | + | 0.192382i | −0.657267 | − | 0.753657i | \(-0.728288\pi\) |
0.324053 | + | 0.946039i | \(0.394954\pi\) | |||||||
\(480\) | 34.7711 | − | 9.97357i | 1.58708 | − | 0.455229i | ||||
\(481\) | 0.0969165 | − | 0.933038i | 0.00441901 | − | 0.0425429i | ||||
\(482\) | − | 15.1890i | − | 0.691841i | ||||||
\(483\) | 21.3608 | + | 20.6244i | 0.971949 | + | 0.938444i | ||||
\(484\) | 4.70405 | + | 13.6923i | 0.213821 | + | 0.622378i | ||||
\(485\) | 46.1352 | + | 26.6361i | 2.09489 | + | 1.20948i | ||||
\(486\) | 2.23318 | − | 12.6958i | 0.101299 | − | 0.575895i | ||||
\(487\) | 4.64583 | + | 2.68227i | 0.210523 | + | 0.121545i | 0.601554 | − | 0.798832i | \(-0.294548\pi\) |
−0.391032 | + | 0.920377i | \(0.627882\pi\) | |||||||
\(488\) | −12.7431 | + | 22.0717i | −0.576853 | + | 0.999139i | ||||
\(489\) | −21.9751 | + | 6.30323i | −0.993747 | + | 0.285042i | ||||
\(490\) | 3.75008 | + | 2.16511i | 0.169411 | + | 0.0978098i | ||||
\(491\) | −17.1649 | − | 29.7305i | −0.774642 | − | 1.34172i | −0.934996 | − | 0.354659i | \(-0.884597\pi\) |
0.160354 | − | 0.987060i | \(-0.448736\pi\) | |||||||
\(492\) | −5.54138 | − | 5.35036i | −0.249825 | − | 0.241213i | ||||
\(493\) | −4.16768 | −0.187703 | ||||||||
\(494\) | −5.70007 | − | 4.13074i | −0.256458 | − | 0.185851i | ||||
\(495\) | 16.0188 | + | 32.1432i | 0.719992 | + | 1.44473i | ||||
\(496\) | −1.79048 | + | 1.03373i | −0.0803948 | + | 0.0464160i | ||||
\(497\) | 22.3177 | + | 38.6555i | 1.00109 | + | 1.73393i | ||||
\(498\) | −21.7220 | − | 5.41399i | −0.973386 | − | 0.242606i | ||||
\(499\) | − | 9.37911i | − | 0.419867i | −0.977716 | − | 0.209933i | \(-0.932675\pi\) | ||
0.977716 | − | 0.209933i | \(-0.0673247\pi\) | |||||||
\(500\) | −7.19286 | + | 12.4584i | −0.321675 | + | 0.557157i | ||||
\(501\) | 8.93230 | − | 35.8382i | 0.399066 | − | 1.60113i | ||||
\(502\) | −10.3358 | −0.461309 | ||||||||
\(503\) | 6.38729 | − | 11.0631i | 0.284795 | − | 0.493280i | −0.687764 | − | 0.725934i | \(-0.741408\pi\) |
0.972560 | + | 0.232654i | \(0.0747411\pi\) | |||||||
\(504\) | −11.2242 | + | 21.1180i | −0.499964 | + | 0.940672i | ||||
\(505\) | −27.9844 | − | 48.4704i | −1.24529 | − | 2.15691i | ||||
\(506\) | −1.55575 | + | 16.0988i | −0.0691617 | + | 0.715678i | ||||
\(507\) | −20.2627 | − | 9.81961i | −0.899896 | − | 0.436104i | ||||
\(508\) | − | 17.1163i | − | 0.759413i | ||||||
\(509\) | 9.99651 | + | 17.3145i | 0.443088 | + | 0.767450i | 0.997917 | − | 0.0645139i | \(-0.0205497\pi\) |
−0.554829 | + | 0.831964i | \(0.687216\pi\) | |||||||
\(510\) | −2.30469 | − | 2.22524i | −0.102053 | − | 0.0985354i | ||||
\(511\) | 19.2505 | − | 33.3429i | 0.851594 | − | 1.47500i | ||||
\(512\) | − | 4.10960i | − | 0.181620i | ||||||
\(513\) | 11.6666 | − | 3.79393i | 0.515094 | − | 0.167506i | ||||
\(514\) | −4.09244 | + | 7.08832i | −0.180510 | + | 0.312652i | ||||
\(515\) | −67.8971 | −2.99191 | ||||||||
\(516\) | −5.14276 | + | 20.6338i | −0.226397 | + | 0.908352i | ||||
\(517\) | −18.7430 | + | 8.53387i | −0.824318 | + | 0.375319i | ||||
\(518\) | 0.312716 | + | 0.541641i | 0.0137400 | + | 0.0237983i | ||||
\(519\) | −4.80962 | − | 16.7679i | −0.211119 | − | 0.736029i | ||||
\(520\) | −28.8979 | − | 20.9418i | −1.26726 | − | 0.918358i | ||||
\(521\) | 24.6791i | 1.08121i | 0.841276 | + | 0.540606i | \(0.181805\pi\) | ||||
−0.841276 | + | 0.540606i | \(0.818195\pi\) | |||||||
\(522\) | −7.83065 | + | 14.7332i | −0.342738 | + | 0.644855i | ||||
\(523\) | −16.7524 | + | 9.67202i | −0.732533 | + | 0.422928i | −0.819348 | − | 0.573296i | \(-0.805664\pi\) |
0.0868151 | + | 0.996224i | \(0.472331\pi\) | |||||||
\(524\) | 0.785909 | − | 1.36123i | 0.0343326 | − | 0.0594658i | ||||
\(525\) | −11.1452 | − | 38.8558i | −0.486417 | − | 1.69581i | ||||
\(526\) | 7.98608 | + | 4.61076i | 0.348210 | + | 0.201039i | ||||
\(527\) | 3.04288 | + | 1.75681i | 0.132550 | + | 0.0765277i | ||||
\(528\) | 2.05966 | − | 0.381175i | 0.0896351 | − | 0.0165885i | ||||
\(529\) | 5.88799 | − | 10.1983i | 0.256000 | − | 0.443404i | ||||
\(530\) | −1.06381 | − | 1.84257i | −0.0462089 | − | 0.0800361i | ||||
\(531\) | −0.643795 | − | 0.342174i | −0.0279383 | − | 0.0148491i | ||||
\(532\) | −9.03338 | −0.391647 | ||||||||
\(533\) | −1.25869 | + | 12.1177i | −0.0545198 | + | 0.524875i | ||||
\(534\) | −14.5837 | + | 4.18311i | −0.631097 | + | 0.181021i | ||||
\(535\) | −17.2310 | − | 29.8450i | −0.744962 | − | 1.29031i | ||||
\(536\) | 7.02049 | + | 12.1599i | 0.303239 | + | 0.525226i | ||||
\(537\) | 4.37588 | − | 17.5569i | 0.188833 | − | 0.757637i | ||||
\(538\) | 0.188348 | 0.00812027 | ||||||||
\(539\) | 3.91623 | + | 2.79547i | 0.168684 | + | 0.120409i | ||||
\(540\) | 23.4750 | − | 7.63396i | 1.01020 | − | 0.328513i | ||||
\(541\) | −3.98233 | −0.171214 | −0.0856068 | − | 0.996329i | \(-0.527283\pi\) | ||||
−0.0856068 | + | 0.996329i | \(0.527283\pi\) | |||||||
\(542\) | 3.66867 | + | 2.11811i | 0.157583 | + | 0.0909805i | ||||
\(543\) | 21.3150 | − | 22.0760i | 0.914715 | − | 0.947372i | ||||
\(544\) | −3.10514 | + | 1.79275i | −0.133132 | + | 0.0768637i | ||||
\(545\) | −24.0643 | −1.03080 | ||||||||
\(546\) | 14.7811 | − | 2.62615i | 0.632572 | − | 0.112389i | ||||
\(547\) | 15.7154i | 0.671940i | 0.941873 | + | 0.335970i | \(0.109064\pi\) | ||||
−0.941873 | + | 0.335970i | \(0.890936\pi\) | |||||||
\(548\) | −1.04721 | − | 1.81382i | −0.0447345 | − | 0.0774824i | ||||
\(549\) | −13.0855 | + | 24.6200i | −0.558474 | + | 1.05076i | ||||
\(550\) | 12.7924 | − | 17.9212i | 0.545470 | − | 0.764162i | ||||
\(551\) | −15.8789 | −0.676463 | ||||||||
\(552\) | 27.1785 | + | 6.77395i | 1.15679 | + | 0.288319i | ||||
\(553\) | −0.796547 | − | 0.459887i | −0.0338726 | − | 0.0195564i | ||||
\(554\) | −0.779086 | −0.0331002 | ||||||||
\(555\) | 0.393360 | − | 1.57824i | 0.0166972 | − | 0.0669926i | ||||
\(556\) | 8.21411 | − | 4.74242i | 0.348356 | − | 0.201123i | ||||
\(557\) | 1.76818 | − | 1.02086i | 0.0749202 | − | 0.0432552i | −0.462072 | − | 0.886842i | \(-0.652894\pi\) |
0.536992 | + | 0.843587i | \(0.319560\pi\) | |||||||
\(558\) | 11.9278 | − | 7.45605i | 0.504943 | − | 0.315640i | ||||
\(559\) | 30.7086 | − | 13.7172i | 1.29884 | − | 0.580177i | ||||
\(560\) | −3.82596 | −0.161676 | ||||||||
\(561\) | −2.31118 | − | 2.70749i | −0.0975782 | − | 0.114310i | ||||
\(562\) | −7.32040 | − | 12.6793i | −0.308792 | − | 0.534844i | ||||
\(563\) | −17.5130 | + | 30.3335i | −0.738087 | + | 1.27840i | 0.215269 | + | 0.976555i | \(0.430937\pi\) |
−0.953356 | + | 0.301849i | \(0.902396\pi\) | |||||||
\(564\) | 3.90290 | + | 13.6068i | 0.164342 | + | 0.572949i | ||||
\(565\) | −31.8280 | − | 18.3759i | −1.33901 | − | 0.773080i | ||||
\(566\) | 1.97645 | − | 3.42330i | 0.0830762 | − | 0.143892i | ||||
\(567\) | −11.4614 | + | 23.5191i | −0.481332 | + | 0.987709i | ||||
\(568\) | 36.4649 | + | 21.0530i | 1.53003 | + | 0.883365i | ||||
\(569\) | 0.907095 | + | 1.57113i | 0.0380274 | + | 0.0658654i | 0.884413 | − | 0.466706i | \(-0.154559\pi\) |
−0.846385 | + | 0.532571i | \(0.821226\pi\) | |||||||
\(570\) | −8.78088 | − | 8.47819i | −0.367791 | − | 0.355112i | ||||
\(571\) | 7.01838i | 0.293710i | 0.989158 | + | 0.146855i | \(0.0469151\pi\) | ||||
−0.989158 | + | 0.146855i | \(0.953085\pi\) | |||||||
\(572\) | −11.7970 | − | 10.4187i | −0.493256 | − | 0.435629i | ||||
\(573\) | −7.35941 | + | 2.11094i | −0.307444 | + | 0.0881858i | ||||
\(574\) | −4.06135 | − | 7.03447i | −0.169518 | − | 0.293613i | ||||
\(575\) | −41.0003 | + | 23.6715i | −1.70983 | + | 0.987170i | ||||
\(576\) | 0.426624 | + | 12.1590i | 0.0177760 | + | 0.506625i | ||||
\(577\) | − | 35.3698i | − | 1.47247i | −0.676728 | − | 0.736233i | \(-0.736603\pi\) | ||
0.676728 | − | 0.736233i | \(-0.263397\pi\) | |||||||
\(578\) | −11.8996 | − | 6.87023i | −0.494958 | − | 0.285764i | ||||
\(579\) | 0.416559 | + | 0.103823i | 0.0173116 | + | 0.00431474i | ||||
\(580\) | −31.9507 | −1.32668 | ||||||||
\(581\) | 39.3486 | + | 22.7179i | 1.63245 | + | 0.942498i | ||||
\(582\) | −14.6835 | + | 15.2077i | −0.608650 | + | 0.630381i | ||||
\(583\) | −0.979648 | − | 2.15161i | −0.0405729 | − | 0.0891107i | ||||
\(584\) | − | 36.3192i | − | 1.50290i | ||||||
\(585\) | −32.3977 | − | 21.7873i | −1.33948 | − | 0.900793i | ||||
\(586\) | 14.0386 | 0.579929 | ||||||||
\(587\) | 0.294905 | + | 0.510791i | 0.0121720 | + | 0.0210826i | 0.872047 | − | 0.489422i | \(-0.162792\pi\) |
−0.859875 | + | 0.510504i | \(0.829459\pi\) | |||||||
\(588\) | 2.29720 | − | 2.37922i | 0.0947350 | − | 0.0981172i | ||||
\(589\) | 11.5934 | + | 6.69344i | 0.477697 | + | 0.275798i | ||||
\(590\) | 0.725386i | 0.0298637i | ||||||||
\(591\) | −1.54936 | + | 6.21635i | −0.0637323 | + | 0.255707i | ||||
\(592\) | −0.0821560 | − | 0.0474328i | −0.00337659 | − | 0.00194948i | ||||
\(593\) | − | 44.3988i | − | 1.82324i | −0.411034 | − | 0.911620i | \(-0.634832\pi\) | ||
0.411034 | − | 0.911620i | \(-0.365168\pi\) | |||||||
\(594\) | −13.9137 | + | 3.08319i | −0.570888 | + | 0.126505i | ||||
\(595\) | 3.25106 | + | 5.63101i | 0.133281 | + | 0.230849i | ||||
\(596\) | 0.849871 | − | 0.490673i | 0.0348121 | − | 0.0200988i | ||||
\(597\) | −2.05592 | − | 7.16759i | −0.0841431 | − | 0.293350i | ||||
\(598\) | −7.17112 | − | 16.0539i | −0.293249 | − | 0.656493i | ||||
\(599\) | 22.1393i | 0.904586i | 0.891869 | + | 0.452293i | \(0.149394\pi\) | ||||
−0.891869 | + | 0.452293i | \(0.850606\pi\) | |||||||
\(600\) | −27.4320 | − | 26.4864i | −1.11991 | − | 1.08130i | ||||
\(601\) | 29.7118 | − | 17.1541i | 1.21197 | − | 0.699730i | 0.248781 | − | 0.968560i | \(-0.419970\pi\) |
0.963188 | + | 0.268829i | \(0.0866368\pi\) | |||||||
\(602\) | −11.2121 | + | 19.4199i | −0.456971 | + | 0.791497i | ||||
\(603\) | 8.14203 | + | 13.0252i | 0.331569 | + | 0.530425i | ||||
\(604\) | −3.59434 | + | 6.22557i | −0.146251 | + | 0.253315i | ||||
\(605\) | 26.0689 | − | 29.9470i | 1.05985 | − | 1.21752i | ||||
\(606\) | 21.3487 | − | 6.12357i | 0.867232 | − | 0.248753i | ||||
\(607\) | 12.5059 | + | 7.22028i | 0.507599 | + | 0.293062i | 0.731846 | − | 0.681470i | \(-0.238659\pi\) |
−0.224247 | + | 0.974532i | \(0.571992\pi\) | |||||||
\(608\) | −11.8306 | + | 6.83041i | −0.479795 | + | 0.277010i | ||||
\(609\) | 23.5218 | − | 24.3616i | 0.953151 | − | 0.987180i | ||||
\(610\) | 27.7403 | 1.12317 | ||||||||
\(611\) | 13.1375 | − | 18.1287i | 0.531487 | − | 0.733407i | ||||
\(612\) | −2.07479 | + | 1.29695i | −0.0838684 | + | 0.0524261i | ||||
\(613\) | 6.24909 | + | 10.8237i | 0.252398 | + | 0.437167i | 0.964186 | − | 0.265228i | \(-0.0854474\pi\) |
−0.711787 | + | 0.702395i | \(0.752114\pi\) | |||||||
\(614\) | −19.1665 | + | 11.0658i | −0.773495 | + | 0.446578i | ||||
\(615\) | −5.10870 | + | 20.4971i | −0.206003 | + | 0.826524i | ||||
\(616\) | 26.3170 | + | 2.54323i | 1.06034 | + | 0.102470i | ||||
\(617\) | −7.25971 | + | 12.5742i | −0.292265 | + | 0.506218i | −0.974345 | − | 0.225060i | \(-0.927742\pi\) |
0.682080 | + | 0.731278i | \(0.261076\pi\) | |||||||
\(618\) | 6.51592 | − | 26.1432i | 0.262109 | − | 1.05163i | ||||
\(619\) | − | 28.1176i | − | 1.13014i | −0.825042 | − | 0.565071i | \(-0.808849\pi\) | ||
0.825042 | − | 0.565071i | \(-0.191151\pi\) | |||||||
\(620\) | 23.3276 | + | 13.4682i | 0.936860 | + | 0.540896i | ||||
\(621\) | 29.9743 | + | 6.36343i | 1.20283 | + | 0.255356i | ||||
\(622\) | −0.180752 | − | 0.313072i | −0.00724751 | − | 0.0125531i | ||||
\(623\) | 30.7927 | 1.23368 | ||||||||
\(624\) | −1.74246 | + | 1.46596i | −0.0697541 | + | 0.0586856i | ||||
\(625\) | −0.689408 | −0.0275763 | ||||||||
\(626\) | 10.0443 | − | 5.79911i | 0.401453 | − | 0.231779i | ||||
\(627\) | −8.80561 | − | 10.3155i | −0.351662 | − | 0.411963i | ||||
\(628\) | −5.61285 | + | 9.72174i | −0.223977 | + | 0.387940i | ||||
\(629\) | 0.161222i | 0.00642834i | ||||||||
\(630\) | 26.0147 | − | 0.912779i | 1.03645 | − | 0.0363660i | ||||
\(631\) | 40.8299 | + | 23.5731i | 1.62541 | + | 0.938432i | 0.985438 | + | 0.170036i | \(0.0543885\pi\) |
0.639975 | + | 0.768396i | \(0.278945\pi\) | |||||||
\(632\) | −0.867650 | −0.0345133 | ||||||||
\(633\) | −5.45713 | + | 21.8951i | −0.216901 | + | 0.870252i | ||||
\(634\) | 0.947270 | − | 0.546907i | 0.0376209 | − | 0.0217204i | ||||
\(635\) | −40.6510 | + | 23.4699i | −1.61319 | + | 0.931373i | ||||
\(636\) | −1.56199 | + | 0.448035i | −0.0619371 | + | 0.0177657i | ||||
\(637\) | −5.20277 | − | 0.540422i | −0.206141 | − | 0.0214123i | ||||
\(638\) | 18.3603 | + | 1.77431i | 0.726893 | + | 0.0702456i | ||||
\(639\) | 40.6750 | + | 21.6186i | 1.60908 | + | 0.855218i | ||||
\(640\) | −25.6901 | + | 14.8322i | −1.01549 | + | 0.586292i | ||||
\(641\) | −15.6699 | − | 9.04702i | −0.618924 | − | 0.357336i | 0.157526 | − | 0.987515i | \(-0.449648\pi\) |
−0.776450 | + | 0.630179i | \(0.782982\pi\) | |||||||
\(642\) | 13.1452 | − | 3.77050i | 0.518798 | − | 0.148810i | ||||
\(643\) | 39.2511 | + | 22.6617i | 1.54791 | + | 0.893688i | 0.998301 | + | 0.0582687i | \(0.0185580\pi\) |
0.549613 | + | 0.835420i | \(0.314775\pi\) | |||||||
\(644\) | −19.5402 | − | 11.2815i | −0.769992 | − | 0.444555i | ||||
\(645\) | 56.0567 | − | 16.0790i | 2.20723 | − | 0.633112i | ||||
\(646\) | 1.04777 | + | 0.604927i | 0.0412238 | + | 0.0238006i | ||||
\(647\) | 9.09155 | − | 5.24901i | 0.357426 | − | 0.206360i | −0.310525 | − | 0.950565i | \(-0.600505\pi\) |
0.667951 | + | 0.744205i | \(0.267172\pi\) | |||||||
\(648\) | 1.72980 | + | 24.6198i | 0.0679531 | + | 0.967157i | ||||
\(649\) | −0.0775317 | + | 0.802289i | −0.00304338 | + | 0.0314926i | ||||
\(650\) | −2.47304 | + | 23.8085i | −0.0970006 | + | 0.933848i | ||||
\(651\) | −27.4427 | + | 7.87154i | −1.07556 | + | 0.308510i | ||||
\(652\) | 15.0446 | − | 8.68599i | 0.589191 | − | 0.340170i | ||||
\(653\) | 39.1789 | − | 22.6199i | 1.53319 | − | 0.885186i | 0.533975 | − | 0.845500i | \(-0.320698\pi\) |
0.999212 | − | 0.0396861i | \(-0.0126358\pi\) | |||||||
\(654\) | 2.30939 | − | 9.26574i | 0.0903043 | − | 0.362319i | ||||
\(655\) | −4.31055 | −0.168427 | ||||||||
\(656\) | 1.06699 | + | 0.616025i | 0.0416588 | + | 0.0240517i | ||||
\(657\) | −1.39324 | − | 39.7081i | −0.0543556 | − | 1.54916i | ||||
\(658\) | 14.9271i | 0.581919i | ||||||||
\(659\) | 8.74287 | − | 15.1431i | 0.340574 | − | 0.589891i | −0.643966 | − | 0.765055i | \(-0.722712\pi\) |
0.984539 | + | 0.175163i | \(0.0560453\pi\) | |||||||
\(660\) | −17.7182 | − | 20.7564i | −0.689681 | − | 0.807943i | ||||
\(661\) | 20.8361 | − | 12.0297i | 0.810430 | − | 0.467902i | −0.0366754 | − | 0.999327i | \(-0.511677\pi\) |
0.847105 | + | 0.531425i | \(0.178343\pi\) | |||||||
\(662\) | 18.5645 | 0.721531 | ||||||||
\(663\) | 3.63823 | + | 1.31884i | 0.141297 | + | 0.0512197i | ||||
\(664\) | 42.8610 | 1.66333 | ||||||||
\(665\) | 12.3866 | + | 21.4542i | 0.480331 | + | 0.831957i | ||||
\(666\) | 0.569938 | + | 0.302920i | 0.0220846 | + | 0.0117379i | ||||
\(667\) | −34.3477 | − | 19.8307i | −1.32995 | − | 0.767847i | ||||
\(668\) | 28.0662i | 1.08591i | ||||||||
\(669\) | −1.73879 | + | 6.97636i | −0.0672254 | + | 0.269722i | ||||
\(670\) | 7.64140 | − | 13.2353i | 0.295213 | − | 0.511324i | ||||
\(671\) | 30.6812 | + | 2.96497i | 1.18443 | + | 0.114461i | ||||
\(672\) | 7.04569 | − | 28.2687i | 0.271793 | − | 1.09049i | ||||
\(673\) | −20.5488 | + | 11.8638i | −0.792097 | + | 0.457317i | −0.840700 | − | 0.541501i | \(-0.817856\pi\) |
0.0486035 | + | 0.998818i | \(0.484523\pi\) | |||||||
\(674\) | 5.84008 | + | 10.1153i | 0.224952 | + | 0.389627i | ||||
\(675\) | −31.0077 | − | 27.9054i | −1.19349 | − | 1.07408i | ||||
\(676\) | 16.7449 | + | 3.51659i | 0.644034 | + | 0.135254i | ||||
\(677\) | 10.8608 | 0.417414 | 0.208707 | − | 0.977978i | \(-0.433074\pi\) | ||||
0.208707 | + | 0.977978i | \(0.433074\pi\) | |||||||
\(678\) | 10.1299 | − | 10.4916i | 0.389038 | − | 0.402928i | ||||
\(679\) | 37.1568 | − | 21.4525i | 1.42595 | − | 0.823270i | ||||
\(680\) | 5.31190 | + | 3.06683i | 0.203702 | + | 0.117607i | ||||
\(681\) | −14.0673 | + | 4.03500i | −0.539061 | + | 0.154622i | ||||
\(682\) | −12.6572 | − | 9.03490i | −0.484669 | − | 0.345964i | ||||
\(683\) | −16.4670 | + | 28.5216i | −0.630091 | + | 1.09135i | 0.357442 | + | 0.933935i | \(0.383649\pi\) |
−0.987533 | + | 0.157414i | \(0.949684\pi\) | |||||||
\(684\) | −7.90496 | + | 4.94139i | −0.302254 | + | 0.188939i | ||||
\(685\) | −2.87186 | + | 4.97421i | −0.109728 | + | 0.190055i | ||||
\(686\) | −11.5528 | + | 6.67002i | −0.441088 | + | 0.254662i | ||||
\(687\) | −19.8872 | − | 19.2016i | −0.758743 | − | 0.732588i | ||||
\(688\) | − | 3.40130i | − | 0.129673i | ||||||
\(689\) | 2.08109 | + | 1.50813i | 0.0792831 | + | 0.0574550i | ||||
\(690\) | −8.40584 | − | 29.3054i | −0.320005 | − | 1.11564i | ||||
\(691\) | −7.96732 | + | 4.59993i | −0.303091 | + | 0.174990i | −0.643831 | − | 0.765168i | \(-0.722656\pi\) |
0.340740 | + | 0.940158i | \(0.389323\pi\) | |||||||
\(692\) | 6.62777 | + | 11.4796i | 0.251950 | + | 0.436390i | ||||
\(693\) | 28.8702 | + | 1.77099i | 1.09669 | + | 0.0672742i | ||||
\(694\) | 19.5004i | 0.740224i | ||||||||
\(695\) | −22.5264 | − | 13.0056i | −0.854474 | − | 0.493331i | ||||
\(696\) | 7.72557 | − | 30.9965i | 0.292837 | − | 1.17492i | ||||
\(697\) | − | 2.09384i | − | 0.0793099i | ||||||
\(698\) | −17.4877 | − | 10.0965i | −0.661917 | − | 0.382158i | ||||
\(699\) | −17.4337 | + | 18.0562i | −0.659404 | + | 0.682947i | ||||
\(700\) | 15.3584 | + | 26.6015i | 0.580491 | + | 1.00544i | ||||
\(701\) | −38.1047 | −1.43919 | −0.719597 | − | 0.694392i | \(-0.755673\pi\) | ||||
−0.719597 | + | 0.694392i | \(0.755673\pi\) | |||||||
\(702\) | 11.4981 | − | 10.3836i | 0.433969 | − | 0.391903i | ||||
\(703\) | 0.614257i | 0.0231671i | ||||||||
\(704\) | 12.2414 | − | 5.57362i | 0.461366 | − | 0.210064i | ||||
\(705\) | 26.9643 | − | 27.9270i | 1.01553 | − | 1.05179i | ||||
\(706\) | 6.66308 | + | 3.84693i | 0.250768 | + | 0.144781i | ||||
\(707\) | −45.0767 | −1.69529 | ||||||||
\(708\) | 0.537573 | + | 0.133985i | 0.0202032 | + | 0.00503545i | ||||
\(709\) | −39.8120 | − | 22.9855i | −1.49517 | − | 0.863238i | −0.495188 | − | 0.868786i | \(-0.664901\pi\) |
−0.999985 | + | 0.00554755i | \(0.998234\pi\) | |||||||
\(710\) | − | 45.8299i | − | 1.71997i | ||||||
\(711\) | −0.948609 | + | 0.0332839i | −0.0355756 | + | 0.00124825i | ||||
\(712\) | 25.1560 | − | 14.5238i | 0.942762 | − | 0.544304i | ||||
\(713\) | 16.7185 | + | 28.9573i | 0.626112 | + | 1.08446i | ||||
\(714\) | −2.48017 | + | 0.711400i | −0.0928179 | + | 0.0266235i | ||||
\(715\) | −8.56835 | + | 42.3038i | −0.320438 | + | 1.58207i | ||||
\(716\) | 13.7495i | 0.513841i | ||||||||
\(717\) | 0.628683 | + | 0.607011i | 0.0234786 | + | 0.0226692i | ||||
\(718\) | 2.07789 | + | 3.59902i | 0.0775463 | + | 0.134314i | ||||
\(719\) | −14.7218 | − | 8.49963i | −0.549030 | − | 0.316983i | 0.199701 | − | 0.979857i | \(-0.436003\pi\) |
−0.748731 | + | 0.662874i | \(0.769336\pi\) | |||||||
\(720\) | −3.34803 | + | 2.09285i | −0.124774 | + | 0.0779960i | ||||
\(721\) | −27.3418 | + | 47.3574i | −1.01826 | + | 1.76368i | ||||
\(722\) | −9.61491 | − | 5.55117i | −0.357830 | − | 0.206593i | ||||
\(723\) | 8.77161 | + | 30.5807i | 0.326220 | + | 1.13731i | ||||
\(724\) | −11.6593 | + | 20.1945i | −0.433314 | + | 0.750522i | ||||
\(725\) | 26.9969 | + | 46.7600i | 1.00264 | + | 1.73662i | ||||
\(726\) | 9.02905 | + | 12.9115i | 0.335099 | + | 0.479192i | ||||
\(727\) | 10.6367 | 0.394494 | 0.197247 | − | 0.980354i | \(-0.436800\pi\) | ||||
0.197247 | + | 0.980354i | \(0.436800\pi\) | |||||||
\(728\) | −26.2437 | + | 11.7228i | −0.972656 | + | 0.434476i | ||||
\(729\) | 2.83565 | + | 26.8507i | 0.105024 | + | 0.994470i | ||||
\(730\) | −34.2352 | + | 19.7657i | −1.26710 | + | 0.731561i | ||||
\(731\) | −5.00600 | + | 2.89022i | −0.185154 | + | 0.106899i | ||||
\(732\) | 5.12384 | − | 20.5579i | 0.189383 | − | 0.759842i | ||||
\(733\) | −0.903764 | −0.0333813 | −0.0166906 | − | 0.999861i | \(-0.505313\pi\) | ||||
−0.0166906 | + | 0.999861i | \(0.505313\pi\) | |||||||
\(734\) | 15.6801 | + | 9.05289i | 0.578762 | + | 0.334148i | ||||
\(735\) | −8.80053 | − | 2.19344i | −0.324612 | − | 0.0809063i | ||||
\(736\) | −34.1212 | −1.25772 | ||||||||
\(737\) | 9.86614 | − | 13.8217i | 0.363424 | − | 0.509129i | ||||
\(738\) | −7.40197 | − | 3.93412i | −0.272470 | − | 0.144817i | ||||
\(739\) | −23.8682 | − | 41.3409i | −0.878006 | − | 1.52075i | −0.853526 | − | 0.521051i | \(-0.825540\pi\) |
−0.0244805 | − | 0.999700i | \(-0.507793\pi\) | |||||||
\(740\) | 1.23598i | 0.0454354i | ||||||||
\(741\) | 13.8617 | + | 5.02480i | 0.509221 | + | 0.184591i | ||||
\(742\) | −1.71356 | −0.0629068 | ||||||||
\(743\) | 0.724160 | − | 0.418094i | 0.0265668 | − | 0.0153384i | −0.486658 | − | 0.873593i | \(-0.661784\pi\) |
0.513225 | + | 0.858254i | \(0.328451\pi\) | |||||||
\(744\) | −18.7065 | + | 19.3744i | −0.685815 | + | 0.710300i | ||||
\(745\) | −2.33069 | − | 1.34562i | −0.0853897 | − | 0.0492998i | ||||
\(746\) | 16.8905 | 0.618405 | ||||||||
\(747\) | 46.8603 | − | 1.64419i | 1.71453 | − | 0.0601578i | ||||
\(748\) | 2.20167 | + | 1.57159i | 0.0805011 | + | 0.0574629i | ||||
\(749\) | −27.7554 | −1.01416 | ||||||||
\(750\) | −3.78606 | + | 15.1904i | −0.138247 | + | 0.554676i | ||||
\(751\) | −11.3098 | − | 19.5892i | −0.412701 | − | 0.714819i | 0.582483 | − | 0.812843i | \(-0.302081\pi\) |
−0.995184 | + | 0.0980237i | \(0.968748\pi\) | |||||||
\(752\) | −1.13207 | − | 1.96080i | −0.0412823 | − | 0.0715031i | ||||
\(753\) | 20.8094 | − | 5.96888i | 0.758338 | − | 0.217518i | ||||
\(754\) | −18.3092 | + | 8.17853i | −0.666781 | + | 0.297844i | ||||
\(755\) | 19.7142 | 0.717473 | ||||||||
\(756\) | 4.12867 | − | 19.4477i | 0.150158 | − | 0.707305i | ||||
\(757\) | −9.88087 | − | 17.1142i | −0.359126 | − | 0.622025i | 0.628689 | − | 0.777657i | \(-0.283592\pi\) |
−0.987815 | + | 0.155632i | \(0.950259\pi\) | |||||||
\(758\) | 0.990299 | − | 1.71525i | 0.0359693 | − | 0.0623006i | ||||
\(759\) | −6.16472 | − | 33.3107i | −0.223765 | − | 1.20910i | ||||
\(760\) | 20.2384 | + | 11.6846i | 0.734123 | + | 0.423846i | ||||
\(761\) | 31.4569 | + | 18.1616i | 1.14031 | + | 0.658358i | 0.946507 | − | 0.322682i | \(-0.104584\pi\) |
0.193803 | + | 0.981041i | \(0.437918\pi\) | |||||||
\(762\) | −5.13569 | − | 17.9047i | −0.186046 | − | 0.648617i | ||||
\(763\) | −9.69056 | + | 16.7845i | −0.350822 | + | 0.607641i | ||||
\(764\) | 5.03840 | − | 2.90892i | 0.182283 | − | 0.105241i | ||||
\(765\) | 5.92519 | + | 3.14922i | 0.214226 | + | 0.113860i | ||||
\(766\) | 7.86930i | 0.284330i | ||||||||
\(767\) | −0.357375 | − | 0.800053i | −0.0129041 | − | 0.0288882i | ||||
\(768\) | −7.11904 | − | 24.8192i | −0.256886 | − | 0.895588i | ||||
\(769\) | −7.14901 | − | 12.3825i | −0.257800 | − | 0.446523i | 0.707852 | − | 0.706360i | \(-0.249664\pi\) |
−0.965652 | + | 0.259838i | \(0.916331\pi\) | |||||||
\(770\) | −11.9250 | − | 26.1910i | −0.429747 | − | 0.943858i | ||||
\(771\) | 4.14599 | − | 16.6346i | 0.149314 | − | 0.599079i | ||||
\(772\) | −0.326222 | −0.0117410 | ||||||||
\(773\) | −12.6620 | + | 21.9313i | −0.455421 | + | 0.788813i | −0.998712 | − | 0.0507315i | \(-0.983845\pi\) |
0.543291 | + | 0.839545i | \(0.317178\pi\) | |||||||
\(774\) | 0.811467 | + | 23.1272i | 0.0291676 | + | 0.831291i | ||||
\(775\) | − | 45.5201i | − | 1.63513i | ||||||
\(776\) | 20.2368 | − | 35.0511i | 0.726458 | − | 1.25826i | ||||
\(777\) | −0.942400 | − | 0.909914i | −0.0338084 | − | 0.0326430i | ||||
\(778\) | −4.22567 | − | 7.31907i | −0.151498 | − | 0.262401i | ||||
\(779\) | − | 7.97755i | − | 0.285825i | ||||||
\(780\) | 27.8918 | + | 10.1107i | 0.998685 | + | 0.362020i | ||||
\(781\) | 4.89845 | − | 50.6886i | 0.175280 | − | 1.81378i | ||||
\(782\) | 1.51095 | + | 2.61705i | 0.0540316 | + | 0.0935855i | ||||
\(783\) | 7.25737 | − | 34.1851i | 0.259357 | − | 1.22168i | ||||
\(784\) | −0.264493 | + | 0.458115i | −0.00944618 | + | 0.0163613i | ||||
\(785\) | 30.7853 | 1.09878 | ||||||||
\(786\) | 0.413673 | − | 1.65974i | 0.0147552 | − | 0.0592010i | ||||
\(787\) | −24.5633 | + | 42.5448i | −0.875586 | + | 1.51656i | −0.0194488 | + | 0.999811i | \(0.506191\pi\) |
−0.856137 | + | 0.516749i | \(0.827142\pi\) | |||||||
\(788\) | − | 4.86825i | − | 0.173424i | ||||||
\(789\) | −18.7414 | − | 4.67110i | −0.667211 | − | 0.166295i | ||||
\(790\) | 0.472193 | + | 0.817863i | 0.0167999 | + | 0.0290983i | ||||
\(791\) | −25.6339 | + | 14.7998i | −0.911438 | + | 0.526219i | ||||
\(792\) | 24.4208 | − | 12.1703i | 0.867754 | − | 0.432451i | ||||
\(793\) | −30.5956 | + | 13.6668i | −1.08648 | + | 0.485321i | ||||
\(794\) | −24.3275 | −0.863350 | ||||||||
\(795\) | 3.20588 | + | 3.09537i | 0.113701 | + | 0.109782i | ||||
\(796\) | 2.83310 | + | 4.90708i | 0.100417 | + | 0.173927i | ||||
\(797\) | −0.534561 | − | 0.308629i | −0.0189351 | − | 0.0109322i | 0.490503 | − | 0.871440i | \(-0.336813\pi\) |
−0.509438 | + | 0.860508i | \(0.670147\pi\) | |||||||
\(798\) | −9.44945 | + | 2.71044i | −0.334507 | + | 0.0959484i | ||||
\(799\) | −1.92393 | + | 3.33234i | −0.0680637 | + | 0.117890i | ||||
\(800\) | 40.2283 | + | 23.2258i | 1.42228 | + | 0.821156i | ||||
\(801\) | 26.9461 | − | 16.8440i | 0.952095 | − | 0.595155i | ||||
\(802\) | 13.9564 | + | 8.05771i | 0.492816 | + | 0.284528i | ||||
\(803\) | −39.9772 | + | 18.2020i | −1.41077 | + | 0.642334i | ||||
\(804\) | −8.39705 | − | 8.10759i | −0.296141 | − | 0.285933i | ||||
\(805\) | 61.8770i | 2.18088i | ||||||||
\(806\) | 16.8153 | + | 1.74664i | 0.592293 | + | 0.0615226i | ||||
\(807\) | −0.379209 | + | 0.108770i | −0.0133488 | + | 0.00382890i | ||||
\(808\) | −36.8253 | + | 21.2611i | −1.29551 | + | 0.747964i | ||||
\(809\) | 8.26616 | + | 14.3174i | 0.290623 | + | 0.503373i | 0.973957 | − | 0.226732i | \(-0.0728042\pi\) |
−0.683334 | + | 0.730105i | \(0.739471\pi\) | |||||||
\(810\) | 22.2657 | − | 15.0292i | 0.782336 | − | 0.528071i | ||||
\(811\) | 26.7650 | 0.939846 | 0.469923 | − | 0.882707i | \(-0.344282\pi\) | ||||
0.469923 | + | 0.882707i | \(0.344282\pi\) | |||||||
\(812\) | −12.8664 | + | 22.2852i | −0.451522 | + | 0.782058i | ||||
\(813\) | −8.60947 | − | 2.14582i | −0.301947 | − | 0.0752573i | ||||
\(814\) | 0.0686372 | − | 0.710249i | 0.00240573 | − | 0.0248942i | ||||
\(815\) | −41.2582 | − | 23.8205i | −1.44521 | − | 0.834394i | ||||
\(816\) | 0.271839 | − | 0.281544i | 0.00951626 | − | 0.00985602i | ||||
\(817\) | −19.0729 | + | 11.0117i | −0.667276 | + | 0.385252i | ||||
\(818\) | 22.5089i | 0.787004i | ||||||||
\(819\) | −28.2427 | + | 13.8234i | −0.986881 | + | 0.483027i | ||||
\(820\) | − | 16.0520i | − | 0.560562i | ||||||
\(821\) | 13.7604 | − | 7.94457i | 0.480241 | − | 0.277268i | −0.240276 | − | 0.970705i | \(-0.577238\pi\) |
0.720517 | + | 0.693437i | \(0.243905\pi\) | |||||||
\(822\) | −1.63967 | − | 1.58315i | −0.0571901 | − | 0.0552186i | ||||
\(823\) | 11.3951 | − | 19.7368i | 0.397207 | − | 0.687982i | −0.596173 | − | 0.802856i | \(-0.703313\pi\) |
0.993380 | + | 0.114873i | \(0.0366463\pi\) | |||||||
\(824\) | 51.5847i | 1.79704i | ||||||||
\(825\) | −15.4060 | + | 43.4690i | −0.536369 | + | 1.51340i | ||||
\(826\) | 0.505948 | + | 0.292109i | 0.0176042 | + | 0.0101638i | ||||
\(827\) | 20.8987i | 0.726718i | 0.931649 | + | 0.363359i | \(0.118370\pi\) | ||||
−0.931649 | + | 0.363359i | \(0.881630\pi\) | |||||||
\(828\) | −23.2704 | + | 0.816492i | −0.808704 | + | 0.0283751i | ||||
\(829\) | 1.27661 | + | 2.21115i | 0.0443384 | + | 0.0767963i | 0.887343 | − | 0.461110i | \(-0.152549\pi\) |
−0.843005 | + | 0.537906i | \(0.819215\pi\) | |||||||
\(830\) | −23.3259 | − | 40.4016i | −0.809652 | − | 1.40236i | ||||
\(831\) | 1.56856 | − | 0.449919i | 0.0544129 | − | 0.0156075i | ||||
\(832\) | −8.58035 | + | 11.8402i | −0.297470 | + | 0.410484i | ||||
\(833\) | 0.899000 | 0.0311485 | ||||||||
\(834\) | 7.16950 | − | 7.42546i | 0.248259 | − | 0.257123i | ||||
\(835\) | 66.6568 | − | 38.4843i | 2.30675 | − | 1.33180i | ||||
\(836\) | 8.38838 | + | 5.98775i | 0.290118 | + | 0.207091i | ||||
\(837\) | −19.7088 | + | 21.8998i | −0.681235 | + | 0.756968i | ||||
\(838\) | −9.36016 | + | 16.2123i | −0.323341 | + | 0.560044i | ||||
\(839\) | 26.0038 | − | 45.0399i | 0.897751 | − | 1.55495i | 0.0673887 | − | 0.997727i | \(-0.478533\pi\) |
0.830362 | − | 0.557224i | \(-0.188133\pi\) | |||||||
\(840\) | −47.9063 | + | 13.7412i | −1.65292 | + | 0.474117i | ||||
\(841\) | −8.11652 | + | 14.0582i | −0.279880 | + | 0.484766i | ||||
\(842\) | −6.76474 | − | 11.7169i | −0.233128 | − | 0.403790i | ||||
\(843\) | 22.0607 | + | 21.3002i | 0.759811 | + | 0.733619i | ||||
\(844\) | − | 17.1468i | − | 0.590218i | ||||||
\(845\) | −14.6087 | − | 44.5909i | −0.502555 | − | 1.53397i | ||||
\(846\) | 8.16533 | + | 13.0624i | 0.280730 | + | 0.449096i | ||||
\(847\) | −10.3898 | − | 30.2422i | −0.356999 | − | 1.03914i | ||||
\(848\) | 0.225091 | − | 0.129956i | 0.00772965 | − | 0.00446272i | ||||
\(849\) | −2.00231 | + | 8.03366i | −0.0687190 | + | 0.275714i | ||||
\(850\) | − | 4.11394i | − | 0.141107i | ||||||
\(851\) | −0.767128 | + | 1.32870i | −0.0262968 | + | 0.0455474i | ||||
\(852\) | −33.9639 | − | 8.46515i | −1.16358 | − | 0.290011i | ||||
\(853\) | 36.8393 | 1.26135 | 0.630677 | − | 0.776045i | \(-0.282777\pi\) | ||||
0.630677 | + | 0.776045i | \(0.282777\pi\) | |||||||
\(854\) | 11.1709 | − | 19.3485i | 0.382259 | − | 0.662092i | ||||
\(855\) | 22.5750 | + | 11.9985i | 0.772049 | + | 0.410341i | ||||
\(856\) | −22.6747 | + | 13.0912i | −0.775005 | + | 0.447449i | ||||
\(857\) | −38.8835 | −1.32823 | −0.664117 | − | 0.747629i | \(-0.731192\pi\) | ||||
−0.664117 | + | 0.747629i | \(0.731192\pi\) | |||||||
\(858\) | −15.4664 | − | 7.35896i | −0.528015 | − | 0.251231i | ||||
\(859\) | −32.7312 | −1.11677 | −0.558387 | − | 0.829581i | \(-0.688580\pi\) | ||||
−0.558387 | + | 0.829581i | \(0.688580\pi\) | |||||||
\(860\) | −38.3776 | + | 22.1573i | −1.30866 | + | 0.755557i | ||||
\(861\) | 12.2393 | + | 11.8173i | 0.417113 | + | 0.402734i | ||||
\(862\) | 1.39156 | − | 2.41026i | 0.0473969 | − | 0.0820938i | ||||
\(863\) | 25.4617 | 0.866726 | 0.433363 | − | 0.901219i | \(-0.357327\pi\) | ||||
0.433363 | + | 0.901219i | \(0.357327\pi\) | |||||||
\(864\) | −9.29783 | − | 28.5915i | −0.316319 | − | 0.972704i | ||||
\(865\) | 18.1760 | − | 31.4817i | 0.618002 | − | 1.07041i | ||||
\(866\) | − | 29.6172i | − | 1.00643i | ||||||
\(867\) | 27.9255 | + | 6.96013i | 0.948398 | + | 0.236379i | ||||
\(868\) | 18.7878 | − | 10.8472i | 0.637701 | − | 0.368177i | ||||
\(869\) | 0.434837 | + | 0.955039i | 0.0147508 | + | 0.0323975i | ||||
\(870\) | −33.4223 | + | 9.58670i | −1.13312 | + | 0.325020i | ||||
\(871\) | −1.90733 | + | 18.3623i | −0.0646275 | + | 0.622184i | ||||
\(872\) | 18.2828i | 0.619134i | ||||||||
\(873\) | 20.7804 | − | 39.0980i | 0.703311 | − | 1.32327i | ||||
\(874\) | 5.75674 | + | 9.97097i | 0.194725 | + | 0.337273i | ||||
\(875\) | 15.8869 | − | 27.5169i | 0.537075 | − | 0.930240i | ||||
\(876\) | 8.32455 | + | 29.0220i | 0.281260 | + | 0.980564i | ||||
\(877\) | 3.21508 | − | 5.56869i | 0.108566 | − | 0.188041i | −0.806624 | − | 0.591065i | \(-0.798708\pi\) |
0.915189 | + | 0.403024i | \(0.132041\pi\) | |||||||
\(878\) | −13.2552 | + | 22.9586i | −0.447340 | + | 0.774816i | ||||
\(879\) | −28.2644 | + | 8.10724i | −0.953336 | + | 0.273450i | ||||
\(880\) | 3.55277 | + | 2.53602i | 0.119764 | + | 0.0854893i | ||||
\(881\) | 4.66499 | − | 2.69334i | 0.157168 | − | 0.0907408i | −0.419353 | − | 0.907823i | \(-0.637743\pi\) |
0.576521 | + | 0.817082i | \(0.304410\pi\) | |||||||
\(882\) | 1.68913 | − | 3.17807i | 0.0568760 | − | 0.107011i | ||||
\(883\) | −1.74325 | −0.0586651 | −0.0293326 | − | 0.999570i | \(-0.509338\pi\) | ||||
−0.0293326 | + | 0.999570i | \(0.509338\pi\) | |||||||
\(884\) | −2.92495 | − | 0.303821i | −0.0983767 | − | 0.0102186i | ||||
\(885\) | −0.418908 | − | 1.46045i | −0.0140814 | − | 0.0490924i | ||||
\(886\) | 6.93929 | + | 12.0192i | 0.233130 | + | 0.403793i | ||||
\(887\) | −24.6417 | − | 42.6807i | −0.827388 | − | 1.43308i | −0.900080 | − | 0.435724i | \(-0.856492\pi\) |
0.0726924 | − | 0.997354i | \(-0.476841\pi\) | |||||||
\(888\) | −1.19907 | − | 0.298855i | −0.0402380 | − | 0.0100289i | ||||
\(889\) | 37.8048i | 1.26793i | ||||||||
\(890\) | −27.3809 | − | 15.8084i | −0.917809 | − | 0.529897i | ||||
\(891\) | 26.2326 | − | 14.2427i | 0.878824 | − | 0.477147i | ||||
\(892\) | − | 5.46344i | − | 0.182930i | ||||||
\(893\) | −7.33018 | + | 12.6962i | −0.245295 | + | 0.424863i | ||||
\(894\) | 0.741790 | − | 0.768274i | 0.0248092 | − | 0.0256949i | ||||
\(895\) | 32.6548 | − | 18.8532i | 1.09153 | − | 0.630195i | ||||
\(896\) | 23.8913i | 0.798153i | ||||||||
\(897\) | 23.7090 | + | 28.1806i | 0.791619 | + | 0.940924i | ||||
\(898\) | − | 4.58874i | − | 0.153128i | ||||||
\(899\) | 33.0252 | − | 19.0671i | 1.10145 | − | 0.635924i | ||||
\(900\) | 27.9912 | + | 14.8772i | 0.933040 | + | 0.495908i | ||||
\(901\) | −0.382537 | − | 0.220858i | −0.0127442 | − | 0.00735784i | ||||
\(902\) | −0.891414 | + | 9.22424i | −0.0296808 | + | 0.307134i | ||||
\(903\) | 11.3588 | − | 45.5738i | 0.377998 | − | 1.51660i | ||||
\(904\) | −13.9611 | + | 24.1813i | −0.464338 | + | 0.804257i | ||||
\(905\) | 63.9488 | 2.12573 | ||||||||
\(906\) | −1.89192 | + | 7.59078i | −0.0628550 | + | 0.252187i | ||||
\(907\) | 3.86028 | + | 6.68620i | 0.128179 | + | 0.222012i | 0.922971 | − | 0.384870i | \(-0.125754\pi\) |
−0.794792 | + | 0.606881i | \(0.792420\pi\) | |||||||
\(908\) | 9.63077 | − | 5.56033i | 0.319608 | − | 0.184526i | ||||
\(909\) | −39.4459 | + | 24.6576i | −1.30834 | + | 0.817842i | ||||
\(910\) | 25.3325 | + | 18.3580i | 0.839764 | + | 0.608562i | ||||
\(911\) | − | 12.0195i | − | 0.398225i | −0.979977 | − | 0.199113i | \(-0.936194\pi\) | ||
0.979977 | − | 0.199113i | \(-0.0638060\pi\) | |||||||
\(912\) | 1.03571 | − | 1.07268i | 0.0342957 | − | 0.0355201i | ||||
\(913\) | −21.4805 | − | 47.1779i | −0.710901 | − | 1.56136i | ||||
\(914\) | −13.9222 | − | 8.03796i | −0.460504 | − | 0.265872i | ||||
\(915\) | −55.8505 | + | 16.0199i | −1.84636 | + | 0.529602i | ||||
\(916\) | 18.1922 | + | 10.5033i | 0.601087 | + | 0.347038i | ||||
\(917\) | −1.73584 | + | 3.00656i | −0.0573224 | + | 0.0992853i | ||||
\(918\) | −1.78121 | + | 1.97922i | −0.0587885 | + | 0.0653240i | ||||
\(919\) | 1.02543 | + | 0.592032i | 0.0338258 | + | 0.0195293i | 0.516818 | − | 0.856096i | \(-0.327117\pi\) |
−0.482992 | + | 0.875625i | \(0.660450\pi\) | |||||||
\(920\) | 29.1852 | + | 50.5503i | 0.962208 | + | 1.66659i | ||||
\(921\) | 32.1981 | − | 33.3477i | 1.06096 | − | 1.09884i | ||||
\(922\) | 3.49756 | 0.115186 | ||||||||
\(923\) | 22.5790 | + | 50.5474i | 0.743197 | + | 1.66379i | ||||
\(924\) | −21.6124 | + | 3.99975i | −0.710996 | + | 0.131582i | ||||
\(925\) | 1.80886 | − | 1.04435i | 0.0594749 | − | 0.0343379i | ||||
\(926\) | 0.532897 | + | 0.923005i | 0.0175121 | + | 0.0303318i | ||||
\(927\) | 1.97884 | + | 56.3980i | 0.0649937 | + | 1.85235i | ||||
\(928\) | 38.9146i | 1.27743i | ||||||||
\(929\) | 11.4306 | − | 19.7984i | 0.375027 | − | 0.649565i | −0.615304 | − | 0.788290i | \(-0.710967\pi\) |
0.990331 | + | 0.138724i | \(0.0443002\pi\) | |||||||
\(930\) | 28.4432 | + | 7.08917i | 0.932688 | + | 0.232463i | ||||
\(931\) | 3.42520 | 0.112256 | ||||||||
\(932\) | 9.53623 | − | 16.5172i | 0.312370 | − | 0.541040i | ||||
\(933\) | 0.544714 | + | 0.525937i | 0.0178331 | + | 0.0172184i | ||||
\(934\) | −3.07485 | − | 5.32580i | −0.100612 | − | 0.174265i | ||||
\(935\) | 0.713566 | − | 7.38390i | 0.0233361 | − | 0.241479i | ||||
\(936\) | −16.5529 | + | 24.6141i | −0.541047 | + | 0.804537i | ||||
\(937\) | 32.3201i | 1.05585i | 0.849291 | + | 0.527925i | \(0.177030\pi\) | ||||
−0.849291 | + | 0.527925i | \(0.822970\pi\) | |||||||
\(938\) | −6.15431 | − | 10.6596i | −0.200945 | − | 0.348047i | ||||
\(939\) | −16.8737 | + | 17.4761i | −0.550653 | + | 0.570312i | ||||
\(940\) | −14.7494 | + | 25.5467i | −0.481073 | + | 0.833243i | ||||
\(941\) | 8.07497i | 0.263237i | 0.991300 | + | 0.131618i | \(0.0420173\pi\) | ||||
−0.991300 | + | 0.131618i | \(0.957983\pi\) | |||||||
\(942\) | −2.95439 | + | 11.8536i | −0.0962594 | + | 0.386212i | ||||
\(943\) | 9.96294 | − | 17.2563i | 0.324438 | − | 0.561943i | ||||
\(944\) | −0.0886142 | −0.00288415 | ||||||||
\(945\) | −51.8492 | + | 16.8611i | −1.68666 | + | 0.548492i | ||||
\(946\) | 23.2840 | − | 10.6014i | 0.757027 | − | 0.344681i | ||||
\(947\) | 13.4187 | + | 23.2418i | 0.436048 | + | 0.755257i | 0.997381 | − | 0.0723334i | \(-0.0230446\pi\) |
−0.561333 | + | 0.827590i | \(0.689711\pi\) | |||||||
\(948\) | 0.693324 | − | 0.198870i | 0.0225181 | − | 0.00645899i | ||||
\(949\) | 28.0211 | − | 38.6668i | 0.909605 | − | 1.25518i | ||||
\(950\) | − | 15.6741i | − | 0.508536i | ||||||
\(951\) | −1.59134 | + | 1.64815i | −0.0516027 | + | 0.0534450i | ||||
\(952\) | 4.27815 | − | 2.46999i | 0.138656 | − | 0.0800529i | ||||
\(953\) | 19.3102 | − | 33.4463i | 0.625519 | − | 1.08343i | −0.362921 | − | 0.931820i | \(-0.618221\pi\) |
0.988440 | − | 0.151611i | \(-0.0484460\pi\) | |||||||
\(954\) | −1.49951 | + | 0.937342i | −0.0485483 | + | 0.0303476i | ||||
\(955\) | −13.8173 | − | 7.97743i | −0.447118 | − | 0.258144i | ||||
\(956\) | −0.575100 | − | 0.332034i | −0.0186001 | − | 0.0107388i | ||||
\(957\) | −37.9902 | + | 7.03075i | −1.22805 | + | 0.227272i | ||||
\(958\) | 3.48182 | − | 6.03069i | 0.112492 | − | 0.194843i | ||||
\(959\) | 2.31297 | + | 4.00618i | 0.0746896 | + | 0.129366i | ||||
\(960\) | −17.6109 | + | 18.2396i | −0.568388 | + | 0.588681i | ||||
\(961\) | −1.14954 | −0.0370820 | ||||||||
\(962\) | 0.316377 | + | 0.708270i | 0.0102004 | + | 0.0228355i | ||||
\(963\) | −24.2882 | + | 15.1826i | −0.782677 | + | 0.489252i | ||||
\(964\) | −12.0875 | − | 20.9361i | −0.389312 | − | 0.674307i | ||||
\(965\) | 0.447316 | + | 0.774774i | 0.0143996 | + | 0.0249409i | ||||
\(966\) | −23.8252 | − | 5.93818i | −0.766563 | − | 0.191058i | ||||
\(967\) | −55.0591 | −1.77058 | −0.885291 | − | 0.465038i | \(-0.846041\pi\) | ||||
−0.885291 | + | 0.465038i | \(0.846041\pi\) | |||||||
\(968\) | −22.7522 | − | 19.8058i | −0.731282 | − | 0.636583i | ||||
\(969\) | −2.45885 | − | 0.612843i | −0.0789896 | − | 0.0196874i | ||||
\(970\) | −44.0531 | −1.41446 | ||||||||
\(971\) | −24.8428 | − | 14.3430i | −0.797242 | − | 0.460288i | 0.0452637 | − | 0.998975i | \(-0.485587\pi\) |
−0.842506 | + | 0.538687i | \(0.818921\pi\) | |||||||
\(972\) | −7.02524 | − | 19.2768i | −0.225335 | − | 0.618303i | ||||
\(973\) | −18.1425 | + | 10.4746i | −0.581622 | + | 0.335800i | ||||
\(974\) | −4.43617 | −0.142144 | ||||||||
\(975\) | −8.77028 | − | 49.3628i | −0.280874 | − | 1.58088i | ||||
\(976\) | 3.38879i | 0.108473i | ||||||||
\(977\) | −27.3007 | − | 47.2861i | −0.873425 | − | 1.51282i | −0.858431 | − | 0.512929i | \(-0.828560\pi\) |
−0.0149944 | − | 0.999888i | \(-0.504773\pi\) | |||||||
\(978\) | 13.1313 | − | 13.6001i | 0.419893 | − | 0.434884i | ||||
\(979\) | −28.5940 | − | 20.4108i | −0.913869 | − | 0.652333i | ||||
\(980\) | 6.89201 | 0.220157 | ||||||||
\(981\) | 0.701346 | + | 19.9887i | 0.0223923 | + | 0.638191i | ||||
\(982\) | 24.5854 | + | 14.1944i | 0.784552 | + | 0.452961i | ||||
\(983\) | −13.2851 | −0.423730 | −0.211865 | − | 0.977299i | \(-0.567954\pi\) | ||||
−0.211865 | + | 0.977299i | \(0.567954\pi\) | |||||||
\(984\) | 15.5727 | + | 3.88133i | 0.496438 | + | 0.123732i | ||||
\(985\) | −11.5620 | + | 6.67534i | −0.368397 | + | 0.212694i | ||||
\(986\) | 2.98469 | − | 1.72321i | 0.0950520 | − | 0.0548783i | ||||
\(987\) | −8.62035 | − | 30.0533i | −0.274389 | − | 0.956607i | ||||
\(988\) | −11.1441 | − | 1.15756i | −0.354540 | − | 0.0368268i | ||||
\(989\) | −55.0090 | −1.74919 | ||||||||
\(990\) | −24.7622 | − | 16.3961i | −0.786994 | − | 0.521104i | ||||
\(991\) | −12.9944 | − | 22.5070i | −0.412782 | − | 0.714959i | 0.582411 | − | 0.812894i | \(-0.302109\pi\) |
−0.995193 | + | 0.0979356i | \(0.968776\pi\) | |||||||
\(992\) | 16.4037 | − | 28.4121i | 0.520818 | − | 0.902084i | ||||
\(993\) | −37.3767 | + | 10.7209i | −1.18611 | + | 0.340219i | ||||
\(994\) | −31.9658 | − | 18.4555i | −1.01389 | − | 0.585372i | ||||
\(995\) | 7.76950 | − | 13.4572i | 0.246310 | − | 0.426621i | ||||
\(996\) | −34.2495 | + | 9.82395i | −1.08524 | + | 0.311284i | ||||
\(997\) | 28.2165 | + | 16.2908i | 0.893625 | + | 0.515935i | 0.875126 | − | 0.483894i | \(-0.160778\pi\) |
0.0184985 | + | 0.999829i | \(0.494111\pi\) | |||||||
\(998\) | 3.87799 | + | 6.71688i | 0.122756 | + | 0.212619i | ||||
\(999\) | −1.32241 | − | 0.280743i | −0.0418393 | − | 0.00888232i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 429.2.t.a.296.20 | yes | 104 | |
3.2 | odd | 2 | inner | 429.2.t.a.296.33 | yes | 104 | |
11.10 | odd | 2 | inner | 429.2.t.a.296.34 | yes | 104 | |
13.4 | even | 6 | inner | 429.2.t.a.329.19 | yes | 104 | |
33.32 | even | 2 | inner | 429.2.t.a.296.19 | ✓ | 104 | |
39.17 | odd | 6 | inner | 429.2.t.a.329.34 | yes | 104 | |
143.43 | odd | 6 | inner | 429.2.t.a.329.33 | yes | 104 | |
429.329 | even | 6 | inner | 429.2.t.a.329.20 | yes | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.t.a.296.19 | ✓ | 104 | 33.32 | even | 2 | inner | |
429.2.t.a.296.20 | yes | 104 | 1.1 | even | 1 | trivial | |
429.2.t.a.296.33 | yes | 104 | 3.2 | odd | 2 | inner | |
429.2.t.a.296.34 | yes | 104 | 11.10 | odd | 2 | inner | |
429.2.t.a.329.19 | yes | 104 | 13.4 | even | 6 | inner | |
429.2.t.a.329.20 | yes | 104 | 429.329 | even | 6 | inner | |
429.2.t.a.329.33 | yes | 104 | 143.43 | odd | 6 | inner | |
429.2.t.a.329.34 | yes | 104 | 39.17 | odd | 6 | inner |